 | John Muller - 1769 - 152 sider
...remaining antecedents is to the product of the remaining confequents, viz. aa : bb : : ce : df, fince the product of the means is equal to that of the extremes. 24. If there be two ranks a, 6, c, d, and e, b, c,f, of four proportionals, two by two, in which either... | |
 | Robert Hamilton - 1777 - 740 sider
...Invertenda. 1 6. Alternando. 1 8. Componenda. 17. Divendo. E. Couvertendo. 12. 19. For, in all thefe cafes, the product of the means is equal to that of the extremes. Thus, we obtain i he fame conciulmns which are demonltrated in the Vth Book of Euclid on other principles.... | |
 | John McGregor (teacher of mathematics.) - 1792 - 532 sider
...: : c—d : d Invertendo, b :a::c:d Convertendo, a : a-\-b : : с : с + d In all thefe varieties, the product of the means is equal to that of the extremes. 54. EQUATIONS. An equation is a propofition afferting the equality of two quantities ; it is ufually... | |
 | Samuel Read Hall - 1832 - 294 sider
...The second arrangement is one 13 : 130 of those which most frequently 180 : 18 occurs. 13 : 18 Since the product of the means is equal to that of the extremes, one product may be taken for the other ; and, as in dividing the product of the extremes by one extreme,... | |
 | Francis Joseph Grund - 1834 - 212 sider
...Moreover, in the two similar triangles, ADE, HDG, the corresponding sides are proportional (page 70, 4thly) ; therefore we have the proportion ED : DG...is equal to that of the extremes (Theory of Prop., Principle 10th), we have HD multiplied by DG, equal to AD multiplied by BD ; consequently, also, half... | |
 | Francis Joseph Grund - 1834 - 204 sider
...Moreover, in the two similar triangles, ADE, HDG, the corresponding sides are proportional (page 70, 4thly) ; therefore we have the proportion ED : DG...geometrical proportion, the product of the means is 108 GEOMETRY. equal to that of the extremes (Theory of Prop., Principle 10th), we have HD multiplied... | |
 | Francis Joseph Grund - 1834 - 202 sider
...Moreover, in the two similar triangles, ADE, HDG, the corresponding sides are proportional (page 70, 4thly) ; therefore we have the proportion ED : DG...3d) ; that is, we have AD: HD = DG: BD; and as, in ever) geometrical proportion, the product of the means ie equal to that of the extremes (Theory of... | |
 | John Playfair - 1836 - 148 sider
...C. X. By Multiplication, RA : RB : : C : D. XI. By Division, ^ : |- : : C : D. Because in each case the product of the means is equal to that of the extremes, and therefore the quantities are proportional. PROP. XII. THEOR. In geometrical progression, the product... | |
 | Silas Totten - 1836 - 360 sider
...the sum of the progression 2, 5, 8, 11, &c. to 31 terms. Ans. 1457. GEOMETRICAL PROPORTIONS. (65.) In every geometrical proportion, the product of the means is equal to the product of the extremes. rZ 1s Take the proportion 12 : 4 = 18 : 6, or ~r =~6- Now, if we reduce... | |
 | Thomas Hill - 1845 - 110 sider
...both terms of a ratio be multiplied by the same number, the ratio is evidently unchanged. 37. In every proportion, the product of the means is equal to that of the extremes. -faJn-i ».j rt~ For if in any proportion each ratio be multiplied by the consequent of the omer, the... | |
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HDG, the corresponding sides are proportional (page 70, 4thly) ; therefore we have the proportion ED : DG =AD : HD (II.) This last proportion has the first ratio common with the first proportion ; consequently the two remaining ratios are in a geometrical... 
