An Elementary Treatise On Geometry Simplified for Beginners Not Versed in Alge

Cover An Elementary Treatise On Geometry Simplified for Beginners Not Versed in Alge
An Elementary Treatise On Geometry Simplified for Beginners Not Versed in Alge
Francis J Francis Joseph Grund
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J- «e : ac, in which the first terra, AB -jr--^> . Instead of being only twice as great as ab^ is now, by the addition of the term ah itself, three times as . Great as ab ; and for the same reason is AC ^f- tzc jthi-ea. Times as ^teat as ac. The two neAV ratios, , • - > AB-|-«6 c a&, and AC 4- ttc : ar, ar6 therefore equal, and- consequently make a proportion. The same would be the case, ' if, instead of adding the second and fourth terms once, you would add them twice respectively to, the firs...t and third terms ; with the only difference, that, the first term, A.^-\-'^ab, would theri be four, times as great as the second term ab. A similar change would take place with regard to the third- term, AC -j- ^ac, which would ihea be four time's as great as the term aj: ; and you would have the proportion AB-}-3«6 :-. Ab — AC. -j- 2ac : ac. If the second term were added . Tlirce times to the first term; the first term, AB -[- ^«^5 would be five times as great as ab ; and the third term, AC -f- 3«c, would also be five times as great ^s aci and so oji.

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