QUA 



then half-shown ; it is bisected, or dicho- 

 tomized. The places of her orbit, where 

 she is either in conjunction or opposition, 

 are her syzygies. 



Quadrature in Geometry. By the qua- 

 drature of a curve is meant the finding 

 of a square equal to the content enclosed 

 by the curve. With regard to the famous 

 problem of the quadrature of the circle — ' 

 since the whole circular area is equal to 

 the rectangle under the radius and a 

 straight line equal to half the circum- 

 ference, the object in squaring the circle 

 is to determine the ratio of the circum- 

 ference to the diameter, and this can only 

 be expressed by infinite series. 



QUADRILA'TERAL {quatuor latera 

 habens). Having four sides ; as applied 

 to a plane geometrical figure, bounded 

 by four straight lines. Such a figure is 

 also called a quadrangle. 



QUADRU'MANA ( quatuor y four, ma- 

 nus, a hand). Four-handed ; the desig- 

 nation of an order of Mammalia, includ- 

 ing the monkey, the lemur, &c., which 

 have a moveable thumb on their lower 

 extremities opposed to the fingers ; all 

 their extremities are, in fact, instru- 

 ments of prehension. 



QUALITY OF PROPOSITIONS. In 

 Logic, propositions are divided according 

 to the quality of their expression, which 

 is here the essential circumstance, into 

 affirmative and negative; and according 

 to the quality of their matter, which is 

 accidental, into true and false. 



QUANTITY {quantus, how much). 

 Quantity is distinguished into continued 

 and discrete. It is continued, when the 

 parts are connected together, and is then 

 termed magnitude, which is the object of 

 geometry. It is discrete, when the parts 

 have an unconnected and independent 

 existence, and then constitutes multi- 

 tude or number, which is the object of 

 arithmetic. 



1. Quantity, negative. The diflSculty 

 attending the use of a minus or negative 

 quantity, in algebraic operations, is re- 

 moved at once by viewing it, as it always 

 must be viewed, in reference to another 

 quantity, which is plus or positive. A 

 debt may be regarded as a negative quan- 

 tity, inasmuch as it is a quantity to be 

 subtracted in case of there being any 

 property (which is positive), from which 

 to subtract it. So also, 



4 — 2 = 2; 

 4 — 2 X 4 — 2 = 4; 



Hence, — 2 is in reality -- (+ 2) ; it 

 279 



QUA 



is the plus or real quantity 4, — the real 

 quantity 2. 



Thus, a — quantity = a — (+ quan- 

 tity). 



2. Quantity fractiorial. It has excited 

 surprise that ^ x i should be ^. Let the 

 question be tried geometrically, and the 

 difl[iculty vanishes. It is only necessary 

 to consider \ as the i of a line 1 ; and 

 the^ as the ^g of the square of the 

 same line. Thus — 



\ linear. 



...^ square. 



Thus, the square of ^ of 1 linear is ^ of 

 1 square ; the square of | linear is J 

 superficial ; and the square of | linear 

 is ^. or i -f •^. All this would be evi- 

 dent if, instead of multiplication, we used 

 the term quadration, or (if admissible) 

 parallelogramization. 



3. Quantity, impossible or imaginary. 

 If an e xpression occur under the form 

 \/ — a, this indicates an impossibility; 

 for it signifies the square root of a nega- 

 tive quantity, which has no existence, ' 

 since there is no quantity, positive or 

 negative, which, being multiplied by 

 itself, gives a negative result. An im- 

 possible quantity, or, in other words, the 

 even root of a negative quantity, may be 

 expressed in the form of a surd, as 

 s/ -^t \/ — 0"^ &c. ; the difference be- 

 tween surd and impossible quantities 

 being that the former have real valufes, 

 though we cannot exactly find them, 

 while there cannot be a quantity, posi- 

 tive or negative, an even power of which 

 would produce a negative quantity. 



QUANTITY OF PROPOSITIONS. 

 In Logic, propositions are divided ac- 

 cording to their quantity, or extent: if 

 the predicate is said of the whole of the 

 subject, the proposition is universal; if 

 of a part of it only, the proposition is 

 particular; in the former, the subject is 

 distributed, or stands for the whole of its 

 significates ; in the latter, it is not dis- 

 tributed, and stands for a part only of its 

 significates. 



QUANTITY and TANTITY. These 

 terms are employed by Mr. Mill, in his 

 " Elements of the Human Mind," as cor- 

 relative, or, as he terms them, connota- 

 tive ; the word quantus, how much, being 



