. Mathematics, compiled from the best authors and intended to be the text-book of the course of private lectures on these sciences in the University at Cambridge [microform]. Cor. Any arc of the primitive circle, as DC, is re-ducible, in this manner, to the similar arc AB of a givenparallel circle. SPHERIC GEOMETRY. 391. -2. When the given small circle is parallel to a right circle. Let XY be the given arcof MN, parallel to EF. Draw two oblique circlesthrough X, Y, the extrem-ities of the given arc, asAXD, A YD, cutting theright circle in O, B, andpassing through the polesA, D. Then OB, reduce
. Mathematics, compiled from the best authors and intended to be the text-book of the course of private lectures on these sciences in the University at Cambridge [microform]. Cor. Any arc of the primitive circle, as DC, is re-ducible, in this manner, to the similar arc AB of a givenparallel circle. SPHERIC GEOMETRY. 391. -2. When the given small circle is parallel to a right circle. Let XY be the given arcof MN, parallel to EF. Draw two oblique circlesthrough X, Y, the extrem-ities of the given arc, asAXD, A YD, cutting theright circle in O, B, andpassing through the polesA, D. Then OB, reducedto the primitive, is equalto TU, and TU is the measure of the arc XY. Cor. By inverting the process any number of degreesmay be set on a small circle, parallel to a right circle, fromany given point. 3. When the given small circle is parallel to an oblique circle. Let XY be the givenarc of XYZ, parallel toABC. Through the poles P,p, and the points X, Y,the extremities of thegiven arc, draw the cir-cles PXp, PYp, perpen-dicular to the given ob-lique circle ABC. ThenOQ. is equal to XY, andto LM. And LM is themeasure of the arc XY. Cor. By inverting theprocess any number ofdegrees may be set on asmall circle, parallel to anoblique circle.
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