 | 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 the value... | |
 | 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. of the ratios... | |
 | John Playfair - Euclid's Elements - 1832 - 358 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...which is compounded of the ratios of their sides. Let AC,CF be equiangular parallelograms having the angle BCDequal to the angle ECG; the ratio of the parallelogram... | |
 | John Playfair - Euclid's Elements - 1833 - 346 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 (14. 1.) ; complete... | |
 | 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... | |
 | Robert Simson - Trigonometry - 1835 - 544 pages
...AB is to CD, as EF to GH. " If, therefore, four straight lines, &c. QED PROP. XXIII. THEOR. See N. Equiangular parallelograms have to one another the...the same with the ratio which is compounded of the ratio of their sides. Let BC, CG be placed in a straight line ; therefore DC Book vI. and'CE are also... | |
 | Euclid - 1835 - 540 pages
...of the sides. And to this demonstration agrees the enunciation which is at present in the text, viz. Equiangular parallelograms 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, in this... | |
 | John Playfair - Euclid's Elements - 1836 - 488 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...the parallelogram AC to the parallelogram CF is the saine with the ratio which is compoundgd of the ratios of their sides. Book VI. Let BC, CG be placed... | |
 | 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...which is compounded of the ratios of their sides. 3. The rectangle contained by the diagonals of any quadrilateral figure inscribed in a circle is equal... | |
 | 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, and to... | |
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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... 
