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 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