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 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