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  2. The Major Tactics of Chess
  3. Tactics Training
  4. Top 10 Tactical Tricks Every Chess Player Must Know

Do lots of tactics problems. I think that tactics are the weapons that grand strategies are based on, and no serious chess player can play without a thorough understanding of tactics in every position. At lower levels, most games are decided by a blunders, and b tactics. If your rating is , those are the two things you should be working on first and foremost. Stephen Tavener. Dallas Tucker. Todd Redden. While not focused on tactics, there is a guy on youtube who does all kinds of videos. He has videos of his own blitz games he is a skilled player , commentaries on grand master games, etc.

He does a pretty good job of explaining the ideas behind positions, and I have learned a lot by watching him. His username is Kingscrusher, and his channel is here. Additionally, he puts up new videos almost every single day, so there is plenty to watch and learn from. But, your question was about tactics.

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You get x amount of seconds to solve a tactical problem. The slower, the more you lose. R 5, a white square, and pawn starts from moves to the three make, Knight must be situated having of double within the octagon radius, or on a white If the. R 4, a black square, and If the pawn starts from square between the. If the. This being understood, it follows that if the pawn starts from 7, a white square, and one move to the make, having Knight must be situated.

Knight can stop a pawn that has the move and is advancing to queen, if the Knight is situated between the Knight's octagon corresponding to the pawn and the Knight's octagon of next lower radius, and on a square of the same color as that occupied by the pawn, or if the Knight is. Tactical Factor P. Whenever a pawn's altitude intersects a Bishop's triangle, then, if the pawn has not crossed the point of intersection, the adverse Bishop wins the given pawn. Knight posted at R 2, R 7, Kt 1, or Kt 8, and having move, is lost, if all the points on its periphery are contained in the sides of an adverse Bishop's triangle.

Obviously, whenever a pawn altitude is coincident with one side of a Rook's quadrilateral, all the points are points of intersection and the to capture when crossing each one. Knight posted at R 2, R 7, Kt 1, or Kt 8, and having move, is lost if all the points on its periphery are contained in the sides of an adverse Rook's quadrilateral. Queen's polygon, then, pawn has not crossed the of the adverse Queen wins the given intersection, point the.

Knight posted at R 2, R 7, Kt 1, or Kt 8, and having move, is lost if all the points on its perimeter are contained in the sides of an adverse Queen's polygon. The Q will equally win if posted at Q 7, K 8, or. Q equally. Whenever the centre of a King's rectangle is contained in the square of progression of a pawn; then the adverse King wins the given pawn. Obviously the King would equally win if posted on any square from the first to the third horizontal inclusive, the King's Rook's file. Knight situated at R 1, and having to move, is lost the points on its perimeter are contained in two.


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Bishop posted at R 1, and with or without the move, the point which it occupies is one of the verti-. Whenever a point of junction is the vertex of a mathematical figure formed by the union of the logistic symbol of a pawn with an oblique, diagonal, horizontal, or vertical from the logistic symbol of any kindred piece then the given combination of two kindred pieces wins any given adverse piece. Obviously it is immaterial what the kindred piece may be, so long as it operates a radius of attack against the point Q 8 nor what the adverse piece may ; ;.

Whenever a piece defending a hostile point of junction is attacked, then, if the point of junction and all points on the periphery of the given piece wherefrom it defends the point of junction, are contained in the. Whenever an adjacent Point of Junction is commanded by a kindred piece, the adverse defending piece is lost. For after the check the white Knight takes an adverse Queen or Rook, regardless of the fact that itself is.

Whenever a Knight and a Bishop occupying squares opposite in color, or of like color but unable to support each other in one move, are simultaneously attacked, then, either with or without the move, the adverse piece wins the given Bishop or the given Knight.

White, having the move, wins by sacrificing pawn by P to Q B 4 ck and thus bringing all the pieces on the perimeter of the same Bishop's triangle. White, having to move, wins, first queening and then with the newly made queen capturpawn the adverse ing pawn. If white has not the move, the black pawn queens without capture.

White, having the move, wins by P to Q 8, and disclosing check from the kindred Bishop. White, either with or without the move, will one of the pawns without capture by the adverse queen Knight. White, either with or without the move, will queen one of the pawns without capture by the adverse Bishop. White, either with or without the move, will one of the pawns without capture by the adverse queen Bishop. White, either with or without the move, will of one the pawns without capture by the adverse queen Rook.

White, either with or without the move, will one of the pawns without capture by the adverse queen King. White, either with or without the move, will the pawns without capture by the adverse of one queen NOTE. If White moves, Black wins all the pawns by moving the King in front of that pawn which advances ; but if Black has to move, one of the pawns will queen without capture against the adverse King. The key of the position is the posting of the King in front of the middle pawn, with one point intervening, when all are in a line and when it is the turn of the pawns to. Offensive always is a diagonal; the Point of Command and the radius are of like color to the Point Material,.

The Point of Command may be either a like or an unlike point. In this situation, the Front Offensive is jective Plane. Command may be either a like or an situated upon either the horizontal and unlike point, The Point of. The Point of Command is an unlike point, and is that point in the Objective Plane at which the given octagon and quadrilateral intersect. The radius is composed of three like and four unlike points ; three unlike points are contained in the diagonals, two unlike and one like points in the vertical, one unlike and two like. The Point of Command is an unlike point, and is that point at which the adverse polygon and.

The radius is horizontal, a diagonal, and an oblique. In evolutions combining a Knight lodgment, the Supporting Factor always must be defended by an Auxiliary Factor. In an evolution against the 0. In each of the foregoing evolutions, there is depicted one of the basic ideas of Tactics the motif of which is either the capture of an opposing piece, the queening of ;. The material manifestation of each idea is given by formations of opposing forces, upon specified points ;. Objective Plane and there is no combination of forces for the producing of either or all of these results possible on the chess-board, in which one or more of these basic ideas is.

Furthermore, the opposing forces, the points at which each is posted, and the result of the given evolution being determinate, it follows that the movements of the given forces equally are determinate, and that the. As the reader has seen, the movements of the pieces in every evolution take the form of straight lines, ex-. The secret of Major Tactics is to attack an adverse piece at a time when it cannot move, at a point where it is defenceless, and with a force that is irresistible.

The first axiom of Major Tactics is A piece exerts no force for the defence of the point upon which it stands. Consequently, so far as the occupying piece cerned, the point upon which a piece solutely defenceless. Hence it is obvious that a pawn defends only a minor diagonal ; that it does not defend a vertical, a horizontal,.

It is admitted that men, whether soldiers or chessplayers, have eyes in their heads,. These two methods, one the crudest and one the most which the sword is lifted to the full height over the head of the unsuspecting and defenceless enemy. From thence they act as unity, for it needs no talent to cut off a man's head who is incapable of resistance, to massacre an army that is hopelessly routed, nor to checkmate the adverse scientific possible, unite at the point at. To attack and capture an enemy who can neither fight. But the second process, compared with the first process, is transcendental; for it consists in surprising and out-manoeuvring two adversaries who have their eyes wide open.

The means by which success is attained in Major is. Tactics is the proper use of time. Hence the student of Major Tactics should be entirely familiar. Assuming, however, that such a defect exists in the opposing force, and that an evolution is valid, it is then necessary to determine the line of operations. See ".

If the object of the Tactics," p. Whatever may be the nature of the geometric plane upon the surface of which it is required in any given situation to execute an evolution, the following conditions always exist The Prime Tactical Factor always is that kindred pawn or piece which captures the adverse Piece Ex:. The Prime Tacti;. The Prime Radii of Offence always extend from the Command, as a common centre, to the perimeter of the geometric symbol appertaining to the Prime Point of Tactical Factor, and upon the vertices of this geometric symbol are to be found the Points Material in every valid evolution.

The Point of Co-operation always is either coincident with a Point Material or is a point on the perimeter of that geometric symbol appertaining to the Prime Tactical Factor of ;. The nature of a Geometric Plane always is determined by the nature of the existing tactical defect the nature ;. Prime Tactical Factor, and the character of the geometric symbol of the Prime Tactical Factor determines the nature of the evolution.

Then, if the number of kindred radii of offence which are directly or indirectly attacking the Point of Command, exceed the number of adverse radii of defence. Franklin K. Young - The Major Tactics of Chess Flag for inappropriate content. Carrusel Anterior Carrusel Siguiente.

Buscar dentro del documento. All rights reserved. Printed by Louis E. Its purpose to elucidate those processes artifice, ; every ruse, trick, play, is upon which and stratagem known in chessis founded consequently, this treatise devoted to teaching the student how to win hostile pieces, to queen his pawns, and to checkmate the adverse king. All the processes herein laid down are determinate, and if the opponent becomes involved in any one of them, he should lose the game.

Each stratagem is illustrative of a principle of Tactics it takes the form of a geometric proposition, and in ; statement, setting and demonstration, exact. Knight Pawn Pawn vs. Pawn Rook Rook y5. Pawn Knight i34 Queen vs. Pawn Queen vs. Knight King vs. Knight Two Knights King and Knight Rook vs.

Pawn Pawn Pawn Pawn vs. Pawn vs. Rook Knight and Pawn vs. King Rook and Pawn vs. King Bishop and Pawn us. Three Pawns Objective Bishop and S. Objective S. Objective Plane 9 Vertical Pieces , Oblique et al. Objective Plane 9 Pieces vs. Objective Plane 9 vs.

Top 10 Most Amazing Tactics Ever in World Championship History

Diagonal Pieces vs. Objective Plane 9 Horizontal Pieces vs. In fact, the prevailing condition in his vicinity was so perturbed that, without even waiting for a response, say nothing of getting any, to your very civil salutation, ; you picked up your green bag again and went into court leaving the old legal luminary, with his head drawn down between his shoulders like a big sea-turtle, to glower at the wall and fight it out with himself.

Furthermore, you may recollect, it was in striking contrast that his and that it Honor blandly regarded your was with an emphasized but strictly arrival, judicial snicker that he inquired after the health of your venerable associate. As a matter of is sitting where you left him, morose and fact, and engaged in frescoing the wainscoting with the ugly, But he he is still nails in his bootheels.

Yet nothing is further from his mind than such low dross as money and such a perish- At this moment he has but a and that is to concoct some Machwhich to paralyze the judge when this evening. But what has turned loose the flood-gates of his bile is that lot of books on the floor beside him. You saw these and thought they were law books ; but they 're not, they are analytical treatises on chess, which are all right if your opponent makes the moves that are laid down for him Your partner make, and all wrong if he does not.

So if you are through with this book ciples, or you had better send it over to him by a boy. An Evolution is that combination of the primary time, locality and force whereby is made a numerical gain ; either by the reduction of the ad- elements verse material, or by the augmentation of the kindred body of chess-pieces. In every locality evolution, and force the primary elements time, are determinate and the proposi- tion always may be mathematically demonstrated.

The mate object of an evolution always is either to checkthe adverse king ; or, to capture an adverse pawn ; or piece or to promote a kindred pawn. The offensive force of a valid at any point against which it is given piece directed ; but the defensive force of a given piece is valid for the support only of one point, except when the points required to be defended are all contained in the perimeter of that geometric figure which appertains to the supporting piece.

All integers of chess force are divided into six classes ; the King, the Queen, the Rook, the Bishop, the Knight and the Pawn. That geometric symbol which is the prime factor in all evolutions which contemplates the action of a Pawn is shown in Fig. Given a Pawn's triangle, the vertices of which are the pawn occupied by one or more adverse pieces, then may make a gain in adverse material.

That geometric symbol which all is the prime factor in is evolutions that contemplate the action of a Knight in Fig. The geometric symbol which is the prime factor in all evolutions which contemplate the action ef a Bishop is shown is in Fig. Given a Bishop's triangle, the vertices of which are the Bishop occupied by one or more adverse pieces, then mav make a gain in adverse material. Given a Rook's quadrilateral, one of whose sides is occupied by two or more adverse pieces or two or more of whose sides are occupied by one or more adverse ; then the pieces material.

That geometric symbol which is a prime factor in all is evolutions that contemplate the action of the Queen shown in Fig. Given one or more adverse pieces situated at the vertices or on the sides of a Queen's polygon, then the Queen may make a gain in adverse material. If the piece has the move, the sub-geometric it is symbol is positive otherwise, negative.

The sub- geometric symbol properly should eventuate into the geometric symbol. The Logistic Symbol typifies its of an integer of chess force the surface of the chess- movement over board and always is combined with the geometric symbol or with the sub-geometric symbol in the execution of a given calculation. The logistic radii of a piece all unite at the centre of its geometric symbol.

The termini of the logistic radii of a piece its always are the vertices of geometric symbol. The logistic radii of a piece always extend from the centre of its geometric symbol to the perimeter. Whenever the geometric symbols appertaining to one or more kindred pieces and to one or more adverse pieces are combined in the same evolution then that ; part of the surface of the chessboard upon which such evolution is executed is termed in this theory a G-eo' metric Plane.

Geometric Planes are divided into three classes I. White to play and win adverse material. White to play and queen a kindred pawn. Whenever the 27 object of a given evolution is to check, figure mate tke adverse king, then that mathematical produced by the combination of the geometric symbols is appertaining to the integers of chess force thus engaged termed a Strategic Plane. White to play and checkmate the adverse king. King in one White having to move checkmates the black move by 1 R K Kt 8 ck. Every plane, whether strategic, tactical, or logistic, : always contains the following topographical features 1.

Zone of Evolution. Kindred Integers. Hostile Integers. Tactical Front. Supporting Factor. Auxiliary Factor. Piece Exposed. Disturbing Integer.

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Primary Origin. Supporting Origin. Auxiliary Origin. Point Material. Point of Interference. White to play and win. White to move. The Zone of Evolution is 31 composed of those verticals, diagonals, horizontals, and obliques which are comprehended in the movements of those pieces which enter The principal figure in any into a given evolution. Zone of Evolution is that geometric pertains to the symbol which apPrime Tactical Factor. White NOTE. A is Kindred Integer is any co-operating piece which contained in a given evolution. White, NOTE. Hostile Integer is any adverse piece which tained in a given evolution.

The Prime Tactical Factor is that kindred Pawn or Piece which in a given evolution either check-mates the adverse King, or captures adverse material, or is promoted to and utilized as some other kindred piece. The Piece Exposed force is 37 whose capture mathematically demonstrated. The Piece Exposed always is situated either upon one of the sides or at one of the vertices of the zone of evolution. Disturbing Factor may or ated within the zone of evolution. The Primary Tactical Factor. The it evolution, as Factor. The Point it evolution, as Factor.

The Point Material is that point which is occupied by adverse piece which, in a given evolution, it is the proposed to capture. The Front Offensive 45 is that vertical, diagonal, horiwhich connects the Primary Origin or zontal, oblique with the Point of Command. The Front Defensive is that vertical, horizontal, diagonal, or oblique which extends from the Point of Com- mand to any point occupied by a hostile integer contained in the geometric symbol which appertains to the Prime Tactical Factor. TJie 47 Supporting Front is that vertical, horizontal, di- agonal, and oblique which unites the Supporting Origin with the Point of Co-operation.

The Point of Command is the centre of that geometsymbol which appertains to the Prime Tactical Factor, and which, when occupied by the latter, wins an adverse piece, or checkmates the adverse king, or enric sures the queening of a kindred pawn. The Point of Command in this evolution is the white square K B 7. The Tactical Objective is that point on the chess-board whose proper occupation is the immediate object of the initiative in any given evolution.

In this evolution the point i. Tactical Plane is that mathematical figure pro- duced by the combination of two or more kindred geometric symbols in an evolution whose object is gain of material. Tactical Planes are divided into three classes, viz. Whenever if evolution in a simple Tactical Plane is valid the opponent has the move, or if not having the move, II. White to play and win the adverse Kt in one move. The decisive point is that at which the geo- metric and the logistic symbols appertaining to the Prime Tactical Factor intersect.

Plane consists of any kindred geometric symbol combined with two or more Points Compound Tactical Material. A of Complex Tactical Plane consists of the combination any two or more kindred geometric symbols with one or more Points Material. No it evolution in a Complex Tactical Plane is valid simplifies the position, either by reducing it to a Compound Tactical Plane in which the opponent, even unless with the move, can offer no resistance or to a Simple Tactical Plane, in which the opponent has not the move nor can offer any resistance.

To reduce a Complex Tactical Plane to a Com- pound Tactical Plane, establish the Supporting Origin at such a point and at such a time that, whether the Supporting Factor be captured or not, the Primary Origin and two or more of the Points Material will become situated on that side of the geometric figure which appertains to the Prime Tactical Factor, the latter III. To reduce a Complex Tactical Plane to a Simple Tactical Plane, eliminate all the Points Material save one, and all the Hostile Integers save one, and establish the Primary Origin and the Point Material upon the same side of that geometric figure which appertains the Prime Tactical Factor, the latter having to move.

White to move and queen pawn without capture by an adverse piece. Compound Logistic Plane is composed of two kin- dred pawn altitudes combined adversely with the geometric figures appertaining to one or more opposing integers of chess force. White to move and queen pawn without capture by King.


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White to move and queen a pawn without capture by the adverse pieces. The black King and the black Bishop are each unable to stop more than one Pawn. Plane Topography. The following topographical features are peculiar to Logistic Planes : 1. Logistic Horizon. Pawn Altitude. Point of Junction. Square of Progression. Corresponding Knights Octagon. Point of Resistance. The Logistic Horizon of White always is is the eighth horizontal that of Black always the first horizontal.

A Point of Junction is that point at which an extremity of a altitude intersects the logistic horizon, queening point of a given pawn. The Corresponding Knight's Octagon is that Knight octagon whose centre is the queening point of the pawn, and whose radius consists of a number of Knight's moves equal to the number of moves to be made by the pawn in reaching its queening point.

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Whenever the net value of the offensive force radiated by a given piece is equal to the net mobility of the Objective Plane ; then, the given piece may checkmate the adverse King. White to play and mate in one move. Whenever the net value by two kindred pieces is of the offensive force radiated equal to the net mobility of the Objective Plane, then the given pieces may checkmate the adverse King.

The following topographical Strategic Planes : features are peculiar to 1. Objective Plane. Objective Plane Commanded. Point of Lodgment. Point of Impenetrability. Like Point. Unlike Point. The Objective Plane is point occupied by the adverse King, together with the imme- composed of the diately adjacent points.

The Objective Plane is commanded when it contains no point open to occupation by the adverse King, by reason of the radii of offence operated against it by hostile pieces. A Like the same posted. Upon these are founded all tactical combinations which are possible in chess all ; play. The first four is propositions govern calculations whose object ; to win adverse pieces the next seven govern all calculaand tions whose object is to queen one or more pawns the final one governs all those calculations whose object is to checkmate the adverse King.

Either to move and win a piece. Black to move, white to win a piece. Black, even with the move, can vacate only one of the vertices of the white geometric symbol. Black, even with the move, cannot vacate the perimeter of the white Knight's octagon consequently the remaining black piece is lost, according to ; Prop. The Knight cannot in one move support the 2 or 8 to Bishop, neither can the Bishop occupy its support the Knight, as these points are commanded by the white Rook. Obviously all those points to which the black can move are commanded by the white Queen.

Knight NOTE. White to move and win a piece. White to move and win of a piece. The Point Command is that centre or vertex where the logistic symbol and the geometric symbol intersect. The diagram illustrative of any position al- ways should contain the logistic symbol and the geometric symbol appertaining to the Prime Tactical Factor. The Point of Command and the points mate- rial are all contained in the same sides of the Rook's quadrilateral. M Black. The Point logistic radii at Q R of Command is White's Q 5 as the 4 do not intersect the centre or a vertex of the geometric symbol.

The white King cannot move to 4 nor to 3, on account of the resistance of the black pieces. Piece attacked. Value of unlike terms. Excess of left-side terms. R Thus, there being no unlike terms, and the number of pieces contained in the left side exceeding the number of pieces contained in the right side, the given piece is undefended. Construct an algebraic inequality having on the left side in the initials of the attacking pieces arranged the order of their potential complements from left to right; and on the right side the initials of the Support- ing Pieces arranged in the order of their potential complements, and also from left to right ; then, If the sum of any number of terms taken in order from left to right on the left side of this inequality is not greater than the sum of the same number of terms taken in order from left to right on the right side, and if none of the terms contained in the left side are less than the like terms contained in the right side, the given piece is defended.

In all cases wherein two or more of the Attacking Pieces operate coincident radfi of offence, or two or more of defence, those pieces of the Supporting Pieces operate coincident radii must be arranged in the con- inequality, not in the order of their potential complements, but in the order of their proximThis applies only to the position ity to the given piece. Either to move and queen a pawn.

White to move, both to queen a pawn. White to move and queen a pawn and prevent the adverse pawn from queening. White to move and queen a pawn. Similarly, describe the figure G H I J K or whose sides are parallel to those of the figure , but whose vertices are two Knight's moves distance from the point o this figure may be called a Knight's octagon of double radius.

In this diagram the white pawn is supposed to start from a point on the King's Rook's file. R 5, a white square, and pawn starts from moves to the three make, Knight must be situated having of double within the octagon radius, or on a white If the octagon of double radius and the octagon of triple radius R 4, a black square, and If the pawn starts from square between the having four moves to make, the Knight must be situated within the octagon of triple radius, or in a black square between the octagon of triple radius and the octagon of quadruple radius In this last case it between the octagon appears that the only square from whence the Knight can stop the pawn is Black's Q R 8.

If the pawn starts first if it squares on the ditions exist as Still K R 2, it may advance two and move, precisely the same constarted from K R 3. This being understood, it follows that if the pawn starts from 7, a white square, and one move to the make, having Knight must be situated KR within the octagon of null radius o , i. From these data a general law may be deduced.

The Knight can stop a pawn that has the move and is advancing to queen, if the Knight is situated between the Knight's octagon corresponding to the pawn and the Knight's octagon of next lower radius, and on a square of the same color as that occupied by the pawn, or if the Knight is next lower radius situated within the Knight's octagon of provided, that the Knight be not en ; prise to the pawn, nor if the pawn is at its sixth square en prise to the pawn after the latter's first move.

Prime Tactical Factor Rook or White to move and. When two verticals opposing pawns are situated on adjacent its Primary Base Line, that side which has not the move wins the adverse pawn. White When the number of horizontals between two opposing pawns situated on adjacent verticals, is odd, that pawn which has not to move wins the adverse pawn ; provided the position is not that of Evolution No. Whenever a pawn iphery of altitude is an adverse Knight's octagon, then, intersected by the perif the pawn has not crossed the point of intersection, the adverse Knight wins the given pawn.

Knight posted if at R1 or its 8, and having to move, is lost all the points on periphery are contained in an adverse Knight's octagon.

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The B will equally win if posted at 8. A Knight posted at and having the move, Bishop's triangle. Whenever a pawn rilateral, then, if the altitude intersects a Rook's quadpawn has not crossed the point of intersection, the adverse Rook wins the given pawn. Knight posted at R1 R or R 8, and having to move, the points on its perimeter are contained in the sides of an adverse Rook's quadrilateral. Knight posted at Kt 2, or Kt 7, and having to move, is lost if all the points on its perimeter are contained in the sides of an adverse Rook's quadrilateral. Black White. Queen vs. Knight posted at R1 or 8, and having to move, is lost if all the points in its perimeter are contained in the sides of an adverse Queen's polygon.

Knight posted at Kt 2 or Kt 7, and having to move, the points on its periphery are contained in the sides of an adverse Queen's polygon. Obviously the King would equally win if posted on any square from the first to the third horizontal inclusive, the King's Rook's file excepted. Knight posted at El or E, 8, and having to move, the points on its periphery are contained in the sides of an adverse King's rectangle. The K would equally win if posted at Q B 6.

Two Pawns vs. The pawns equally win 7. Obviously it is immaterial what the kindred piece may be, so long as it operates a radius of attack against the point Q 8 nor what the adverse piece may ; ; be, nor what its the white pawn position, so long as at Q 7. Pawn and Knight Black. Whenever a piece defending a hostile point of junction is attacked, then, if the point of junction and all points on the periphery of the given piece wherefrom it defends the point of junction, are contained in the geometric symbol which appertains to the adverse piece, the piece defending a hostile point of junction is lost.

Bishop and Pawn Black. Obviously, it is immaterial what ; may be either the kindred piece or the adverse piece the white pawn queens by force, and the kindred piece wins the is adverse piece, which, of course, the newly made Queen. Eook and Pawn Black.

M " White.

Top 10 Tactical Tricks Every Chess Player Must Know

White wins ; easily kindred pawn the black Rook from followed by by R to K 7 supporting the R to K 8 upon the removal of 1. A Knight having to move periphery are is lost if all the points in its commanded by adverse pieces. Knight and Bishop Black.


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Rook and Knight Black. Queen and Knight Black. White wins if Black has to move. King and Knight Black. Queen and Bishop Black. White wins either with or without the move. Queen and Rook Black. King and Queen Black, vs. Two Black. Whenever two adverse pieces are posted on the verti- ces of a pawn's triangle and on the same horizontal, then if neither piece commands the remaining vertex, the given pawn, having to move, wins one of the adverse pieces.

The pawn would posted at K 3. Rook and Black. Whenever two adverse pieces are situated on the perimeter of a Knight's octagon, then if neither piece commands the centre point nor can support the other only by occupying another point on the perimeter of the said octagon, the given Knight, having to move, wins one of the adverse pieces. King and Queen. For after the check the white Knight takes an adverse Queen or Rook, regardless of the fact that itself is thereby lost. Two Pawns. King and Pawn.

King and Knight. Two Knights. White wins by to 5 as neither of the ad- verse pieces are able to support the other in a single move. Whenever two Knights are simultaneously attacked by an adverse piece, then if one of the Knights has to move, the adverse piece wins one of the given Knights. Knight and Bishop. Rook and Knight. Rook and Bishop. Knight and Pawn. Bishop and Pawn. JL White.