| John Muller - Mathematics - 1769 - 152 pages
...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 - Business mathematics - 1777 - 740 pages
...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.) - Mathematics - 1792 - 532 pages
...: : 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 - Arithmetic - 1832 - 294 pages
...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 - Geometry, Plane - 1834 - 212 pages
...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 - Geometry, Plane - 1834 - 204 pages
...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 - Geometry, Plane - 1834 - 202 pages
...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 - Geometry - 1836 - 148 pages
...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 - Algebra - 1836 - 360 pages
...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 - Arithmetic - 1845 - 110 pages
...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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