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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... "
First lessons in Plane Geometry. Together with an application of them to the ... - Page 211
by Francis Joseph Grund - 1830 - 12 pages
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A New System of Mathematics: Containing Plane Geometry; General ...

John Muller - Mathematics - 1769 - 154 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...
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An Introduction to Merchandize: Containing a Compleat System of Arithmetic ...

Robert Hamilton - Algebra - 1777 - 364 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....
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A Complete Treatise on Practical Mathematics: Including the Nature and Use ...

John McGregor (teacher of mathematics.) - Mathematics - 1792 - 431 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...
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The Arithmetical Manual

Samuel Read Hall - Arithmetic - 1832 - 288 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,...
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An Elementary Treatise on Geometry: Simplified for Beginners Not ..., Part 1

Francis Joseph Grund - Geometry, Plane - 1834 - 190 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...
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An Elementary Treatise on Geometry: Simplified for Beginners Not ..., Part 1

Francis Joseph Grund - Geometry, Plane - 1834 - 206 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...
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An Elementary Treatise on Geometry: Simplified for Beginners Not ..., Part 1

Francis Joseph Grund - Geometry, Plane - 1834 - 190 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...
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The Element of Geometry

John Playfair - Geometry - 1836 - 114 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...
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A New Introduction to the Science of Algebra...

Silas Totten - Algebra - 1836 - 362 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...
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An Elementary Treatise on Arithmetic: Designed as an Introduction to Peirce ...

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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