 | Horatio Nelson Robinson - Algebra - 1879 - 332 pages
...quantities be in proportion, they will be in proportion by INVERSION ; that is, the second will be to the first, as the fourth to the third. Let a : b = c : d. Then by formula (A), \ = § (1). oa Clearing of fractions, be = ad . . . (2). Hence by Prop. II., b : a... | |
 | Aristotle - Aesthetics - 1883 - 114 pages
...cutting draining and draining cutting, both 6 being to take something away : by (4) analogy I mean when the second is to the first as the fourth to the third, as then one may use the fourth for the second or the second for the fourth, sometimes even adding that... | |
 | Aristotle - Aesthetics - 1885 - 118 pages
...cutting draining und draining cutting, both 6 being to take something awuy : by (4) analogy I mean when the second is to the first as the fourth to the third, as then one may use the fourih for the second or the second for the fourth, sometimes even adding that... | |
 | James Edward Oliver - Algebra - 1887 - 434 pages
...&) . THKOE. 7. If four numbers be proportional, they are proportional : (a) Inversely : the second to the first as the fourth to the third. Let a : b = с : d, then will b : a = d : c. For ••• ad =bc, [th. 6 .-. b:a = d:c. QED [th. G cv. (b) Alternately:... | |
 | George Albert Wentworth - Geometry - 1890 - 296 pages
...quantities are in proportion, they will be in proportion by inversion ; that is, the second term will be to the first as the fourth to the third. Let a: b = c:d. To prove b : a = d : c. Now be = ad. § 295 Divide each member of the equation by ac. Then *=£... | |
 | George Albert Wentworth - Geometry - 1894 - 456 pages
...quantities are in proportion, they will be in, proportion by inversion ; that is, the second term will be to the first as the fourth to the third. Let a •. b = c : d. To prove b:a = d:c. Now be = ad. § 295 Divide each member of the equation by ac. Then £ = £ ac or,... | |
 | Judith H. Anderson - History - 2005 - 344 pages
...transference resulting from analogy as being "possible whenever there are four terms so related that the second is to the first, as the fourth to the third; for one may then put the fourth in place of the second, and the second in place of the fourth."45 This... | |
 | Joseph Ray - Algebra - 1848 - 248 pages
...quantities are in proportion, they will be in proportion by INVERSION ; that is, the second icil! be to the first as the fourth to the third. Let a : b : : c : d. By Art. 244, ad=be. Dividing both sides by b, j:=eDividing both sides by d, i.—jThat is, 6 : a :... | |
 | Joseph Ray - Algebra - 1848 - 252 pages
...quantities are in proportion, they will be in proportion by INVERSION ; that is, the second will be to the first as the fourth to the third. Let a : b : : c : d. By Art. 244, ad=bc. Dividing both sides by 6, ~~T=CDividing both sides by d, T— jThat is, b : a :... | |
| |
Componendo, by composition ; when there are four proportionals, and it is inferred that the first together with the second, is to the second, as the third together with the fourth, is to the fourth. 
