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 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 A B 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 A B is the ...
Σελίδα 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 ...
Σελίδα 201
... half of the circle . Upon the square E F G H erect a pyramid of the same altitude with the cone ; this pyramid is greater than half of the cone . For , if a square be described about the circle , and a pyramid be erected upon it ...
... half of the circle . Upon the square E F G H erect a pyramid of the same altitude with the cone ; this pyramid is greater than half of the cone . For , if a square be described about the circle , and a pyramid be erected upon 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