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 99
... ratio of that which it has to the second . When three magnitudes are continual proportionals , the ratio of the first to the third is compounded of two equal ratios - viz . , the ratio of the first to the second , and the ratio of the ...
... ratio of that which it has to the second . When three magnitudes are continual proportionals , the ratio of the first to the third is compounded of two equal ratios - viz . , the ratio of the first to the second , and the ratio of the ...
Σελίδα 120
... ratio of A to C , is equal to the ratio which is compounded of the ratios of D to E , and of E to F , which is the ratio of D to F. A.B.C. D.E.F. Because there are three magnitudes , A , B , and C , and other three D , E , and F , which ...
... ratio of A to C , is equal to the ratio which is compounded of the ratios of D to E , and of E to F , which is the ratio of D to F. A.B.C. D.E.F. Because there are three magnitudes , A , B , and C , and other three D , E , and F , which ...
Σελίδα 212
... ratio of that which their diameters have . Let A B C and D E F be two spheres , of which the diameters are BC and EF . The sphere A B C has to the sphere D E F the triplicate ratio of that which BC has to EF . For , if not , the sphere ...
... ratio of that which their diameters have . Let A B C and D E F be two spheres , of which the diameters are BC and EF . The sphere A B C has to the sphere D E F the triplicate ratio of that which BC has to EF . For , if not , the sphere ...
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A B and CD A B C D A B is equal adjacent angles altitude angle ABC angle B A C 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 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