 | Euclid, Thomas Tate - 1849 - 120 pages
...the opposite angles, &c. QED PROP. XXHL THEOR. Upon the same straight line, and upon the same-side of it, there cannot be two similar segments of circles, not coinciding with one another. If it be possible, let the two similar segments of circles, viz. ACB, ADB, be upon the... | |
 | Euclides - 1853 - 146 pages
...angles. Therefore the opposite angles, &c. QED PROP. XXIII. — THEOREM. Upon the same straight line, and upon the same side of it, there cannot be two similar segments of circles, not coinciding with one another. If it be possible, let the two similar segments of circles, viz. ACB, ADB, be upon the... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...Therefore, the opposite angles, etc. <;. £. i). PROPOSITION XXIII. TIIEOR. Upon the same straight line, and upon the same side of it, there cannot be two similar segments of circles, not coinciding with one another. If it be possible. let the two similar segments of circles, viz. ACB' ADB be upon the... | |
 | Euclides - Geometry - 1853 - 176 pages
...Therefore the opposite angles, &c. QED PROPOSITION XXIII. — THEOREM. Upon the same straight line and wpon the same side of it, there cannot be two similar segments of circles not coinciding imth one another. IF it be possible, let the two similar segments of circles, viz. a С b, adb be upon... | |
 | Euclides - Geometry - 1853 - 334 pages
...just been shewn to be equal to it : which is impossible. Therefore on the same straight line and on the same side of it, there cannot be two similar segments of a circle, not coinciding with one another. Which was to be proved. PEOP. XXIV. THEOE. Similar segments... | |
 | William Somerville Orr - Science - 1854 - 534 pages
...interior and opposite angle (U). PROPOSITION XXIII.— THEOREM. Ujion the same straight line (AB), and on the same side of it, there cannot be two similar segments of circles not coinciding with one another. For if it be supposed possible, let ACB, ADB be two similar segments, not coinciding with... | |
 | Euclides - 1855 - 270 pages
...equal to its interior angle, which is impossible (I. 16). Therefore upon the same straight line, and on the same side of it there cannot be two similar segments of circles which do not coincide. QED Corollary. — If there be two segments of circlea on the same base or chord,... | |
 | Sandhurst roy. military coll - 1859 - 672 pages
...the straight Jine which is made up of the half and the part produced 4. Upon the same straight line, and upon the same side of it there cannot be two similar segments of circles not coinciding with one another. Voluntary Portion. 1 . Solve the equations : (1) &*"- 7*+ 2=0. x-4 ff-3 <2>^ r + —2... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...angles. Therefore, the opposite angles, &c. QED PROPOSITION XXIII. THEOREM. Upon the same straight line, and upon the same side of it, there cannot be two similar segments of circles, not coinciding with one another. If it be possible, upon the same straight line AB, and upon the same side of it, let there... | |
 | Euclides - 1860 - 288 pages
...exterior to the interior, which is impossible (I. 16); therefore on the same straight line, and on the same side of it, there cannot be two similar segments of circles not coinciding. Similar segments of circles upon equal straight lines are equal to one another. Given AEB and CFD two... | |
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Upon the same straight line, and upon the same side of it, there cannot be two similar segments of circles, not coinciding with one another. If it be possible. let the two similar segments of circles, viz. ACB' ADB be upon the same side of the same straight... 
