...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...

...has been (hewn (in Cor. td Theo. 13. Sect, i.) that Triangles on the fame Bafe, and between the fame Parallels are equal : But if you would draw a Map from the Bafes and Perpendiculars, it is evident that you muft know at what Part of the Bafe the Perpendicular...

...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...base the perpendicular was taken in order to set it oft' in its due position ; and hence the map is easily constructed. PROBLEM XVI. To determine the area...

...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...must know at what part of the base the perpendicular was1 takeri$ in order to set it off' in its due position ; and hence the map is easily constructed....

...shewn (in cor. to theo. 13. geom.J that triangles on the same base, and between the same parallels arc equal ; but if you would draw a map from the bases...position ; and hence the map is easily constructed. PROB. XVI. To determine the area of a fiiece of ground, having the •map given, by reducing it to...

...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,...

...was taken : since it has been shewn (in cor. to theo. 18. sect. 1.) that triangles on the same bane, and between the same parallels are equal : but if...position ; and hence the map is easily constructed. PROB. To determine the area of a piece of ground, having the map given, by reducing it to one triangle...

...at what 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...position ; and hence the map is easily constructed. PROS. XVI. PL. 8. 2ig. 5. To determine the area of a piece of ground, having the maft given, by reducing...

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

...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,...