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 E B , BFC , CG D , and D H A , 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 E B , BFC , CG D , and D H A , 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 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