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 110
... less , less ( V. Def . 5 ) . Again , because C is to D , E is to F , and H and K are taken equimultiples of C and E ; and M L and N , of D and F. If H be greater than M , K is greater than N ; if equal , equal ; and if less , less . But ...
... less , less ( V. Def . 5 ) . Again , because C is to D , E is to F , and H and K are taken equimultiples of C and E ; and M L and N , of D and F. If H be greater than M , K is greater than N ; if equal , equal ; and if less , less . But ...
Σελίδα 116
... less , less . Let A , B , and C be three magnitudes , and D , E , and F other three , which taken two and two have the same ratio ; viz . , as A is to B , so is D to E ; and as B is to C , so is E to F. If A be greater than C , D is ...
... less , less . Let A , B , and C be three magnitudes , and D , E , and F other three , which taken two and two have the same ratio ; viz . , as A is to B , so is D to E ; and as B is to C , so is E to F. If A be greater than C , D is ...
Σελίδα 211
... less sphere . Also the other planes between the quadrants BX and K X do not meet the less sphere . From the point A draw A I perpendicular to the plane of the quadrilateral S OPT , and join IO . În the same manner , as it was proved of ...
... less sphere . Also the other planes between the quadrants BX and K X do not meet the less sphere . From the point A draw A I perpendicular to the plane of the quadrilateral S OPT , and join IO . În the same manner , as it was proved of ...
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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