Jak. 12, 1S83.] 



KNO^VLEDGE 



29 



D B 



Hy IV. ' ! '- L 



Sq. onCB = sq. ob CD + sq. on DB + rect. CD, DB + rectCD, DB 

 = sq. on CD + rect. CB, DB + rect. CD, DB (bv III) 

 = 8q. on CD + rect. AC, DB + rect. CD, DB{VCB = AC) 

 = 8q. on CD + rect. AD, DB (by I) 

 Pbop. TI. — Let the straight line AB he hisected in C and produced 

 to D : then the rectangle AD, DB, together leith the sq. on CB, shall 

 i'O equal to the sq. on CD. 



A C B D 



By IV. ! I—- ! ! 



Sq. onCD = sq. on CB + sq. on BD + rect. CB, BD +rcct. CB, BD 

 = 8q. on CB + rect. CD, BD + rect. CB, BD 

 = sq. on CB + rect. AD, DB (by I, VCB = AC). 

 Pbop. VII. — Let the straight line, AB, be divided into any tu'o 

 (III if .s ill C: then the sqs. on AB, BC are equal to tu-ice the rectangle 

 AB, BC, together with the sq. on AC. 



A C B 



By IV. Sq. on AB = sq. on AC + 8q on BC + 2 rect. AC, CB 

 .•.' sqs. on AB, BC =sq. on AC + 2 sq. on BC + 2 rect. AC,CB 

 = sq. on AC + 2 rect. AB, BC (by III.). 

 Pbop. Vin. — Let the straight line, AB, he divided into any (no 

 parts in C, and produced to D, so that BD = BC, then shall the sq. 

 on AD le equal to four times the rect. AB, BC, together ivith the sq. 

 m AC. 



A C B D 



Bv IV., sq. on AD = sq. on AC + sq. on DC + 2 rect. AC, CD 

 = 8q. on AC+4sq. on CB+4rect. AC, CB 



(by Cor. to IV., and I.) 

 = 8q. on AC + 4 rect. AB, BC (by III.). 

 Pkop. IX. — Let the straight line, AB, be divided into («•■< eq>'al 

 parts in C, and into two unequal parts in D ; then the sqs. on AD, 

 I'B, are together double the sqs. on AC, CD. 



A C D B 



By IV., sq. on AD =8q. on AC + sq. on CD + 2 rect. AC, CD ; .*. 

 sqs.onAD,BD = sq. on AC + sq. on CD + 2 rect. CB, CD -rsq.on DB 

 = 8<i.on AC + eq. onCD + 8q.onCB + sq. on CD (by VII.) 

 = 2sq. on AC-r2 8q. on CD (•.•CB = AC) 

 Pbop. X. — Let the straight line, AB, be bisected in C, and produced 

 to D: then the squares on AD, DB shall be double of the squares on 

 AC, CD. 



A C B D 



By IV. sq. on AD = sq. on AC + sq. on CD + 2 rec. AC, CD ; .". 



sqs.onAD, BD = sq. on AC + sq. on CD + 2 rect. CB, CD + sq. on BD 

 = sq. on AC + sq. on CD + sq. on CB + sq. on CD (by VII.) 

 = 2 8q. on AC + 2sq. onCD (•.•CB = AC). 

 (To be e<mttnue<i.) 



0UV aaa&i'st column. 



By " Five of Clcbs." 



1J17HEX we consider the conduct of the hand, as a whole, we 

 »f recognise the object of the various leads and returns and 

 continuations of the opened suit ; and we see how much those 

 partners usually gain who play a combined game, and how much is 

 lost in the long run by those who seek only to play their own hand. 



Thus, between my partner's hand and mine there is probably one 

 suit, at least, which may be established and brought in, with proper 

 care in the play of our hands. That one of us who has the hrst 

 lead has usually no choice bat to show his long suit, whether it is 

 weak or not. The other, when his time to lead arrives, must decide 

 whether he will show his own suit or adopt his partner's. By 

 showing his own he usually does what the first leader had not 

 done — he indicates a certain degree of strength. By returning his 

 partner's, he says, " I have no suit strong enough to justify me in 

 showing it ; probably tlie adversaries have more strength in it than 

 you and I have j let us combine to establish and bring in your suit 

 if we can." The player who returns his partner's suit in this way, 

 before showing his own, should bear this in mind ; for his partner's 

 play will undoubtedly be guided by this supposed evidence of 

 weakness in other suits. 



It is for this reason, also, that the first discard is so carefully to 

 be attended to. It helps to show your partner where your strength 

 lies, by indicating where you are weakest, — in the case we are 

 dealing with at present (that strength in trumps has not been 



declared on either side), and also if strength has been declared in 

 your favour. If your partner has shown his strong suit, and one 

 of the enemies his, your declaration of your weakest suit may not 

 necessarily show your partner in what suit you are strong ; for your 

 weakest suit may lie his, or that of the adversary who has already 

 declared his strength ; your longest suit (your strength if yon have 

 a strong suit) may Ho either in tho third plain suit, or in trumps. 

 But he learns, at any rate, that you are weak in one suit, and is 

 saved from tho bad effects which would have arisen had he looked 

 for strength from yon in that suit. 



Every indication on the part of the enemy must be carefully 

 watched, to show where stiength lies and where weakness. 



In the early progress of tho play, indications may be afforded 

 cither on the one hand of sufficient strength in trumps, with a strong 

 suit between you and your partner, to enable you at once to take 

 a commanding position, or, on the other hand, of such broken forces 

 that the best chance you have is to pick up whatever tricks may 

 come in your way, without any thought of establishing a suit, and 

 scarcely a hope of preventing the adversaries from doing so. Of 

 the former case we do not speak now, because it will be considered 

 fully in our chapter on Leading Trumjis. In the latter case play 

 carefully to the score, finessing where it seems the only way to save 

 the game, but refraining from even the most promising finesse where 

 a single trick saves the game. Euff at every opportunity if so weak 

 in trumps that you cannot hope to disarm the enemy; but, if you 

 have three or four small trumps and your partner early shows 

 extreme weakness, you sometimes do well to keep your trumps to 

 draw two for one, when yon get the chance. 



But, in ordinarj- cases, play a steadfast game, neither too boldly 

 aiming at a great game with moderate force, nor too anxiously 

 playing to save tho game when, with care, you may maintain an 

 equal fight. 



It is to gain full command of your own suit that you play the lowest 

 of a long head-sequence, so that, if partner has the winning card, 

 he may play it. The same principle holds as the suit is continued, 

 and applies to shorter sequences. Thus, suppose that after at least 

 one round of a suit you hold second and third best and one or 

 more small ones, your partner having only two, one of which may 

 be the best ; if you play the second best, you draw the best from 

 the enemy ; but if your partner holds the best, he would not put it 

 on yotu- second best. Even if he knows you to hold the third best, 

 he would infer from your playing the highest that you wished 

 him to leave the trick to you. In fact, if ho knew you 

 to hold both second and third best, he would be apt to 

 regard the lead of second best under the circumstances as 

 involving a request to pass the trick. But the third round 

 falling to him, you cannot have your suit returned to you. 

 Therefore, in such a case you should play the third best, which 

 your partner will take, and returning the small one, leave you 

 free to continue the suit. When trumps are out, and your suit 

 otherwise established (that is your partner's King-card only against 

 you), neglect of this precaution is ruinous. In like manner you 

 must constantly be on the watch to get rid of a winning card in 

 your partner's suit which would be apt to obstruct it. The game 

 in our last number affords a good illustration of this point. If 

 attention had not been paid to this rule, the game would not have 

 been won. 



(To be continued.) 



^UV 



CI)ed9 Column. 



By Mephisto. 



CHESS is never more attractive than when it is played with 

 ingenuity. It is tho originality of chess which charms and 

 attracts devotees to our nobk game. Soundness in play ought, of 

 course, to be allied to ingenuity, but we hold that the latter quality 

 ought to predominate. The mission of chess is to amuse, therefore 

 it logically follows that ingenuity (which amuses) ought to be 

 primarily cultivated. Chess does not differ in this respect from 

 music and other arts, in which the great desideratum is to combine 

 truth (soundness) with beauty (ingenuity). A successful combina- 

 tion of these two principles must necessarily result in the highest 

 standard of excellence being attained. Unfortunately, however, 

 we have many adherents to each principle by itself, but only very 

 few who combine both qualities in a very high degree. We have 

 Wagner and Verdi, Steinitz and Blackbumc. But we have also 

 had (though very seldom) a Handel, who combines in his works the 

 perfected principles of both Wagner and Verdi. We likewise can 

 refer to Morphy, whose play is a glorious combination of the 

 different styles of Steinitz and Blackburne. 



Steinitz, "during his tour in the United States, played a match 

 with Martinez, a Philadelphian player, and the former won every 



