The Elements of Geometry: Or, The First Six Books, with the Eleventh and Twelfth of EuclidCassell, Petter, and Galpin, 1859 - 212 Seiten |
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Seite 49
... half and the part produced . Let the straight line A B be bisected in C , and produced to the point D. The squares ... half a right angle ( I. 32 ) . For the same reason , each of the angles CEB and EBC is half a right angle . Therefore ...
... half and the part produced . Let the straight line A B be bisected in C , and produced to the point D. The squares ... half a right angle ( I. 32 ) . For the same reason , each of the angles CEB and EBC is half a right angle . Therefore ...
Seite 190
... half , and from the remainder more than its half ; and so on : there will at length remain a magnitude less than the least of the proposed magnitudes . Let A B and C be two unequal magnitudes , of the same kind , of which AB is the ...
... half , and from the remainder more than its half ; and so on : there will at length remain a magnitude less than the least of the proposed magnitudes . Let A B and C be two unequal magnitudes , of the same kind , of which AB is the ...
Seite 200
... half of the segment of the circle which contains it ( XII . 2 ) . Erect prisms upon each of these triangles , of the same altitude with the cylinder ; each of these prisms is greater than half of the cylindric segment which contains it ...
... half of the segment of the circle which contains it ( XII . 2 ) . Erect prisms upon each of these triangles , of the same altitude with the cylinder ; each of these prisms is greater than half of the cylindric segment which contains it ...
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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