 | John Playfair - Circle-squaring - 1819 - 350 pages
...to EA. Join BE, CD ; then the triangle BDE is equal to the triangle CDE (37. 1.), because they are on the same base DE, and between the same parallels DE, BC : but ADE is another triangle, and equal magnitudes have, to the same, the same ratio (7. 5.) ; therefore,... | |
 | Euclid, Robert Simson - Geometry - 1821 - 514 pages
...CE to EA. Join BE, CD; then the triangle BDE is equal to the triangle CDE (37. 1.), because they are on the same base DE, and between the same parallels DE, BC; ADE is another triangle, and equal magnitudes, have to the same the same ratio (7. 5.); therefore,... | |
 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...as CE to EA. Join BE, CD; then the triangle RUH U equal to the triangle CDE, (87.) because they, are on the same base DE, and between the same parallels DE, BC : ADE is another triangle, and equal magnitude! hare to the same, the lame ratio ; (7. 5.) therefore,... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...to EA. * 37. 1. Join BE, CD ; then the triangle BDE is equal* to the triangle CDE, because they are on the same base DE, and between the same parallels DE, BC : ADE is another triangle; and equal magnitudes have to the * 7- 5. same* the same ratio ; therefore,... | |
 | John Playfair - Geometry - 1836 - 148 pages
...Join BE, CD ; then the triangle BDE is equal to the triangle CDE (Cor. 1. 15. 2.), because they are on the same base DE, and between the same parallels DE, BC. ADE is another triangle, and equal magnitudes have to the same, the same ratio (13. 4.) ; therefore... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...CE to EA. Join BE, CD ; then the triangle BDE is equal to the triangle CDE (I. 37), because they are on the same base DE, and between the same parallels DE, BC. But ADE is another triangle, and equal magnitudes have to the same the same ratio (V. 7) ; therefore,... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...ABC; BD: DA : : CE: EA. Join BE, CD. Then (I. 37.) the triangles BDE, CDE are equal, because they are on the same base DE, and between the same parallels, DE, BC. Now ADE is another triangle, and ( V. 7.) equal magnitudes have to the same, the same ratio ; therefore,... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...to EA. Join BE, CD ; then the triangle BDE is equal to the triangle CDE (37. 1 .), because they are on the same base DE and between the same parallels DE, BC : but ADE is another triangle, and equal magnitudes have, to the same, the same ratio (7. 5.) ; therefore,... | |
 | Euclides - 1838 - 264 pages
...CE to EA. «3, 1 Join BE, CD ; then the triangle BDE is equal' to the triangle CDE, because they are on the same base DE, and between the same parallels DE, BC: *Def.7.5. ADE is another triangle; therefore,* as the triangle BDE is to the triangle ADE, so is the... | |
 | Euclides - Geometry - 1841 - 378 pages
...DA, as CE to EA. Join BE, CD; then the triangle BDE is equal* to the triangle CDE, because they are on the same base DE, and between the same parallels DE, BC: but ADE is another triangle, and equal magnitudes have the same ratio to the same magnitude; * therefore,... | |
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... section shall be parallel to the remaining side of the triangle. Let DE be drawn parallel to BC, one of the sides of the triangle ABC: then BD shall be to DA, as CE to EA. Join BE, CD; then the triangle BDE is equal... 
