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The elements of Euclid : viz, the first six books, together with the eleventh and twelfth : the errors, by which Theon, or others, have long ago vitiated these books, are corrected, and some of Euclid's demonstrations are restored : also, The book of Euclid's data, in like manner corrected (1834)

Euclid, Euclid, Simson, Robert, 1687-1768 · Philadelphia : Desilver & Thomas · leaf 348

An illustration from The elements of Euclid : viz, the first six books, together with the eleventh and twelfth : the errors, by which Theon, or others, have long ago vitiated these books, are corrected, and some of Euclid's demonstrations are restored : also, The book of Euclid's data, in like manner corrected, 1834, leaf 348
IGK, DAC, at the vertices of theisosceles triangles GHK, ADC are equal to one another, these tri-angles are similar; and because GL, AF are perpendicular to thebases HK, DC, as HK to GL, so is (4. 6. 22. 5.) (DC to AF, andso is) the rectangle DC, CE to the rectangle AF, CE; but as GLto its half, so… … 546 EUCLID S DATA. Cor. And if a triangle have a given angle, the space by whichthe square of the straight line which is the difference of the sideswhich contain the given angle is less than the square of the thirdside, shall have a given ratio to the triangle. This is demon-strated the same way as…

Mathematics, Greek · Geometry · Trigonometry

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