...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...

...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...

...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...

...I shall 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 equal: a theorem which appears, from a very simple construction, to be only a few steps removed from the fourth...

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...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 ; a theorem which appears, from a very simple construction, to be only a few steps removed from the...

...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...

...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,...

...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,...

...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...