| Aristotle - 1883 - 95 Seiten
...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 - 1885 - 95 Seiten
...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, Lucien Augustus Wait, George William Jones - 1887 - 412 Seiten
...&) . 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 - 1890 - 437 Seiten
...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 - 1894 - 437 Seiten
...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 - 2005 - 324 Seiten
...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 - 1848 - 240 Seiten
...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 - 1848 - 240 Seiten
...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 :... | |
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