 | Euclides - 1848 - 52 pages
...straight lines be proportionals, those straight lines shall be proportionals. PROP. XXIII. THEOREM. Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides. PROP. XXIV. THEOREM. The parallelograms about the diameter of any parallelogram, are similar to the... | |
 | 1851 - 268 pages
...have their sides about their equal angles reciprocally proportional. .3. Equiangular paralellograms have to one another the ratio which is compounded of the ratios of their sides. SECTION IV. 1. Upon a given base to describe an isosceles triangle equal to a given rectangle. 2. To... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...to GH; ABis to CD, as EF to GIL If therefore four straight lines, etc. QED PROPOSITION XXIII. THEOU. 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 BCD equal to the angle ECG : the ratio of... | |
 | Sir James Kay-Shuttleworth - Church and education - 1853 - 554 pages
...to one angle of the other, have their sides about their equal angles reciprocally proportional. 3. Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides. Section 4. 1. Upon a given base to describe an isosceles triangle equal to a given rectangle. 2. To... | |
 | Sir James Kay-Shuttleworth - Church and education - 1853 - 524 pages
...their sides about their equal angles reciprocally proportional. 3. Equiangular parallelograms hare to one another the ratio which is compounded of the ratios of their sides. Section 4. 1. Upon a given base to describe an isosceles triangle equal to a given rectangle. . 2.... | |
 | Euclides - Geometry - 1853 - 334 pages
...THEOE. If two parallelograms have one angle of the one equal to one angle of the other : then they shall have to one another the ratio which is compounded of the ratios of each pair of sides about the equal angles. Let ABCD, EFGH be two parallelograms, having the angle ABC... | |
 | Robert Potts - 1855 - 1050 pages
...angles to each of them in that point; these three straight lines are in cue and the same plane. 14. Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides. Draw a straight line perpendicular to the plane of a triangle such that if any point in it be joined... | |
 | Euclides - 1855 - 270 pages
...described upon them, are also continual proportionals ; and amversely. PROP. XXIIL THEOREM. taugu/ar parallelograms have to one another the ratio which is compounded of the ratios of their sides Let AC and CF be equiangular parallelograms, having the angle BCD equal to the angle EC G. The ratio... | |
 | Euclides - 1855 - 230 pages
...similarly situated. They are to one another as the rectangles under their bases and altitudes. They have to one another the ratio which is compounded of the ratios of their sides. Their sides about the eqnal angles are reciprocally proportional. They are equal to one another. They... | |
 | Noble Heath - 1855 - 468 pages
...multiplying the base by its perpendicular height or altitude, (103,) it is evident that the areas of any two parallelograms have to one another the ratio which is compounded of the ratios of their bases and altitudes. Hence we deduce the following properties : 1. Parallelograms of equal base and... | |
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Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. 
