 | 1867 - 964 pagina’s
...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 pagina’s
...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 pagina’s
...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 pagina’s
...which experience is equally incompetent to disprove or to confirm ? 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,... | |
 | Dugald Stewart - 1821 - 706 pagina’s
...the case of equal triangles which differ in figure, this expedient of ideal superposition cannot be directly and immediately employed to evince their...a very simple construction, to be only a few steps rcnjoved from the fourth of the same book, in which the supposed application of the one triangle to... | |
 | Robert Gibson - 1821 - 594 pagina’s
...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... | |
 | Walter Henry Burton - 1828 - 84 pagina’s
...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 - 442 pagina’s
...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 pagina’s
...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 pagina’s
...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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In like manner, when it is said, that " triangles on the same base, and between the same parallels, are equal... 
