 | John Playfair - Geometry - 1836 - 148 pages
...equal to the angle ECG ; the ratio of the parallelogram AC to the parallelogram CF, is the same with the ratio which is compounded of the ratios of their sides. Let BC, CG, be placed in a straight line ; therefore DC and CE are also in a straight line (2. 1.) ; and... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...&c.* Cor. Triangles which have one angle of the one equal, or supplemental, to one angle of the other, have to one another the ratio which is compounded of the ratios of the sides containing those angles. For, if BD and EG be joined, the triangles BCD, ECG being (I. 84.)... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...equal to the angle ECG ; the ratio of the parallelogram AC to the parallelogram CF, is the same with the ratio which is compounded of the ratios of their sides. Let EC, CG, be placed in a straight line ; therefore DC and CE are also in a straight line (I. 14) ; and... | |
 | Robert Simson - Geometry - 1838 - 434 pages
...equal to GH ; AB is to CD, as EF to GH. If, therefore, four straight lines, &c. QED PROP. XXIII. THEOR. EQUIANGULAR parallelograms have to one another the...CF be equiangular parallelograms, having the angle * See Note. BCD equal to the angle ECG : the ratio of the parallelogram AC to the parallelogram CF,... | |
 | English literature - 1840 - 528 pages
...the Moon's rotation exactly equal to the motion in its orbit. WEDNESDAY. Jan. 8 ...... 9 to llj. 1. EQUIANGULAR parallelograms have to one another the...which is compounded of the ratios of their sides. 2. Every solid angle is contained by plane angles which are together less than four right angles. 3.... | |
 | Education - 1840 - 468 pages
...at the heginning of the year. SENATE-HO.USE EXAMINATION. WEDNESDAY. Jan. 8, 1840 ____ 9 to 1IJ. 1. EQUIANGULAR parallelograms have to one another the...which is compounded of the ratios of their sides. 2. Every solid angle is contained hy plane angles which tire together less than four right angles.... | |
 | Euclides - Geometry - 1841 - 378 pages
...having the angle BCD equal to the angle ECG: the parallelogram AC shall have to the parallelogram CF, the ratio which is compounded of the ratios of their sides. Let BC, CG be placed in a straight line; therefore DC and CE are also in a straight line;* and complete... | |
 | Euclides - 1842 - 316 pages
...c, D be four straight lines, and if л : в : : c : D, then A* : B* : : c* : D*. PROP. XXIII. THEOR. EQUIANGULAR parallelograms have to one another the ratio which is compounded of the ratio of their sides. Let AC, CF be equiangular parallelograms, having the angle BCD equal to the angle... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...equal to the angle ECG ; the ratio of the parallelogram AC to the parallelogram CF, is the same with the ratio which is compounded of the ratios of their sides. Let BC, CG be placed in a straight line ; therefore DC and CE are also in a straight line (14. 1.); complete... | |
 | Euclides - 1845 - 546 pages
...to CD, as EF to GH. (v. 7-) If, therefore, four straight lines, &c. QED PROPOSITION XXIII. THEOREM. Equiangular parallelograms have to one another the...parallelograms, having the angle BCD • equal to the angle ECG. Then the ratio of the parallelogram AC to the parallelogram CF, shall be the same with the ratio which... | |
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Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. Let AC, CF be equiangular parallelograms having the angle BCD equal to the angle ECG ; the ratio of the parallelogram AC to the parallelogram CF... 
