The Elements of Geometry: Or, The First Six Books, with the Eleventh and Twelfth of EuclidCassell, Petter, and Galpin, 1859 - 212 σελίδες |
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Σελίδα 98
... magnitudes is meant that each magnitude is taken or repeated the same number of times . Now , by taking equimultiples of the first and third of the supposed magnitudes , and equimultiples of the second and fourth of the same magnitudes ...
... magnitudes is meant that each magnitude is taken or repeated the same number of times . Now , by taking equimultiples of the first and third of the supposed magnitudes , and equimultiples of the second and fourth of the same magnitudes ...
Σελίδα 101
... magnitudes , of which the same or equal magnitudes are equi- multiples , are equal to one another . This axiom means that equi - submultiples of the same or of equal magnitudes , are equal . III . A multiple of a greater magnitude is ...
... magnitudes , of which the same or equal magnitudes are equi- multiples , are equal to one another . This axiom means that equi - submultiples of the same or of equal magnitudes , are equal . III . A multiple of a greater magnitude is ...
Σελίδα 112
... Magnitudes have the same ratio to one another which their equimultiples have . Let A B be the same multiple of C , that D E is of F. C is to F , A B is to DE . Divide A B into magnitudes , each equal to C , viz . , A G , GH , and HB ...
... Magnitudes have the same ratio to one another which their equimultiples have . Let A B be the same multiple of C , that D E is of F. C is to F , A B is to DE . Divide A B into magnitudes , each equal to C , viz . , A G , GH , and HB ...
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A B and CD A B C D A B is equal adjacent angles altitude angle ABC base B C bisected Cassell's centre circle A B C circle ABCD circumference cone cylinder D E F described diagonal diameter draw equal angles equal Ax equal Const equiangular equimultiples Euclid exterior angle given rectilineal given straight line gnomon greater homologous Illustrated inscribed join less Let A B C multiple opposite angles parallelopiped pentagon perpendicular polygon prism proposition pyramid Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment solid A B solid angle sphere squares of AC straight line drawn straight lines A B THEOREM three plane angles touches the circle triangle A B C triplicate ratio twice the rectangle vertex Wherefore