 | 1867 - 964 pages
...г, as we will proceed to show. The reader will remember that in Problem XXIV (page 308) it was shown that triangles on the same base and between the same parallels are equal to one another, and that triangles on equal bases and between the same parallels are also equal to... | |
 | Robert Gibson - 1806 - 486 pages
...of the bases the perpendicular was taken : since it has been shewn (in cor. to theo. 13, sect. 1.) that triangles on the same base, and between the same parallels are equal : but if you would draw a map from the bases and perpendiculars, it is evident that you must know at... | |
 | Robert Gibson - 1808 - 482 pages
...part of the base the perpendicular was taken : since it has been shewn (in cor. to theo. 13. seel. 1.) that triangles on the .same base, and between the same parallels are equal : but if you would draw a map from the bases and perpendiculars, it is evident that you must know at... | |
 | Dugald Stewart - 1814 - 560 pages
...quantities, equality is identity." (Met. x. c. 3. For wjino remarks on this last passage, See Note (F.) ately employed to evince their equality ; but the demonstration...only appeal to the thirty-seventh proposition of the Grst book, in which it is proved that triangles on the same base, and between the same parallels, are... | |
 | Robert Gibson - 1821 - 594 pages
...part of the base the perpendicular was taken : since it has been shown (in cor. to theo. 13. geom.) that triangles on the same base, and between the same parallels, are equal ; but if you would draw a map from the bases and perpendiculars, it is evident that you must know at... | |
 | Dugald Stewart - 1822 - 572 pages
...the ca¿e of equal triangles which differ in figure, this expedient of ideal superposition cannot be directly and immediately employed to evince their...the first book, in which it is proved that triangles 0:1 the same base, and between the same parallels, are equal ; a theorem which appears, from a very... | |
 | Walter Henry Burton - 1828 - 84 pages
...next proposition is very important, and the truth of it is not obvious at first sight. Parallelograms on the same base, and between the same parallels, are equal. A.. I perceive that it is so in your first figure, where the diagonal of one parallelogram serves for the... | |
 | Dugald Stewart - 1829 - 418 pages
...which experience is equally incompetent to disprove or to confirm 1 In like manner, when it is said, that " triangles on the same base, and between the same parallels are equal," do we feel ourselves the less ready to give our assent to the demonstration, if it should be supposed,... | |
 | John Playfair - 1829 - 210 pages
...triangle is half of a parallelogram on the same base and between the same parallels (41. 1.), and all triangles on the same base and between the same parallels are equal (37.1.); consequently ka b will denote the number of square feet in any plane triangle. Hence the surface... | |
 | Robert Gibson - 1832 - 290 pages
...part of the base the perpendicular was taken ; since it has been shown (in cor. to theo. 1 3 geom.) that triangles on the same base and between the same parallels are equal : but if you would draw a map from ' the bases and perpendiculars, it is evident that you must know... | |
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I shall only appeal to the thirty- seventh proposition of the first book, in which it is proved that triangles on the same base, and between the same parallels, are equal... 
