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 73
... fore , in equal circles , & c . Q. E. D. Corollary . - Equal angles either at the centre or the circumference of the same circle , stand upon equal arcs . Exercise . -Parallel chords in a circle intercept ( take between them ) equal ...
... fore , in equal circles , & c . Q. E. D. Corollary . - Equal angles either at the centre or the circumference of the same circle , stand upon equal arcs . Exercise . -Parallel chords in a circle intercept ( take between them ) equal ...
Seite 116
... fore D has to E a greater ratio than C has to B ( V. 13 ) . Because B is to C , as E to F ( Hyp . ) . Therefore , by inversion , C is to B , as F is to E ( V. B ) . But D was shown to have to E a greater ratio than C has to B. Therefore ...
... fore D has to E a greater ratio than C has to B ( V. 13 ) . Because B is to C , as E to F ( Hyp . ) . Therefore , by inversion , C is to B , as F is to E ( V. B ) . But D was shown to have to E a greater ratio than C has to B. Therefore ...
Seite 200
... fore the prisms upon the triangles A EB , BFC , CG D , and D HA , are greater than half of the cylindric segments which contain them . Therefore , if each of the arcs be bisected , and straight lines be drawn from the points of ...
... fore the prisms upon the triangles A EB , BFC , CG D , and D HA , are greater than half of the cylindric segments which contain them . Therefore , if each of the arcs be bisected , and straight lines be drawn from the points of ...
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Häufige Begriffe und Wortgruppen
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