 | John Martin Frederick Wright - Astronomy - 1831 - 282 pages
...axis intercepted between the origin and the normal. TRINITY COLLEGE, 1829. 1 . EQUIANGULAR / — 73 have to one another the ratio which is compounded of the ratios of their sides. 2. If two straight lines be J_ to the same plane, they are || to one another. 3. Required... | |
 | Industrial arts - 1831 - 532 pages
...and join AB and DE. The parallelograms CF and CO are evidently equiangular ; they have, therefore, to one another the ratio which is compounded of the ratios of their sides (23 of VI); that is, the ratio which is IMPROVED MODE OF PRESERVING BEBH FROM SOCRINC.... | |
 | Euclides - 1834 - 518 pages
...ratios that are the same with the ratios of the sides. And to this demonstration agrees the enunciation have to one another the ratio which is compounded of the ratios of the sides ; for the vulgar reading, " which is compounded of their sides," is absurd. But, iu this edition,... | |
 | Euclid - 1835 - 540 pages
...AB is to CD, as EF to GH. " If, therefore, four straight lines, &c. QED PROP. XXIII. THEOR. Sec N. 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... | |
 | John Playfair - Geometry - 1836 - 148 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 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... | |
 | John Martin Frederick Wright - Mathematics - 1836 - 776 pages
...which the other sides of the triangle have to one another. Shew that the converse is also true. 2. Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. 3. The rectangle contained by the diagonals of any quadrilateral figure inscribed in a... | |
 | Mathematics - 1836 - 488 pages
...straight lines be proportionals, those straight lines shall be proportionals. XXIII. Equian. guiar parallelograms have to one another the ratio which is compounded of the ratios of their sides. XXIV. The parallelograms about the diameter of any parallelogram, are similar to the whole,... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...equal to GH; therefore AB : CD : : EF : GH ; wherefore, if four straight lines, &c. PROP. XXIII. THEOR. 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 angles BCD, ECG equal : AC has to... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...squares are proportional, and conversely. For squares are similar figures. PROPOSITION XXIII. THEOREM. Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. Let AC, CF, he equiangular parallelograms, having the angle BCD equal to the angle ECG... | |
 | 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 ratio which is compounded of the ratios of their sides.* Let AC, CF be equiangular parallelograms, having the angle * See Note. BCD equal to the... | |
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Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. 
