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 13
... straight line ; that is , to divide it into two equal parts . Let A B be the given straight line . It is required to divide it into two equal parts . Describe upon AB ( 1.1 ) an equilateral triangle ABC , and bisect ( I. 9 ) the angle A ...
... straight line ; that is , to divide it into two equal parts . Let A B be the given straight line . It is required to divide it into two equal parts . Describe upon AB ( 1.1 ) an equilateral triangle ABC , and bisect ( I. 9 ) the angle A ...
Σελίδα 133
... straight line similarly to a given divided straight line , that is , into parts proportional to the parts of the given divided straight line . Let A B be the given straight line to be divided , and A C the given straight line , divided ...
... straight line similarly to a given divided straight line , that is , into parts proportional to the parts of the given divided straight line . Let A B be the given straight line to be divided , and A C the given straight line , divided ...
Σελίδα 159
... A B and CD . In like manner , it may be proved , that FE makes right angles with every other straight line meeting it in that plane . But a straight line is at right angles to a plane when it makes ... straight lines BOOK XI . 159 PROP . V.
... A B and CD . In like manner , it may be proved , that FE makes right angles with every other straight line meeting it in that plane . But a straight line is at right angles to a plane when it makes ... straight lines BOOK XI . 159 PROP . V.
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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