 | Augustus De Morgan - 1831 - 108 pàgines
...of one equal to two angles of the others, and the interjacent side equal, are equal in all respects. Parallelograms on the same or equal bases, and between the same parallels, are equal. The explanation of this is as follows : the whole proposition is divided into distinct assertions,... | |
 | Robert Gibson - 1832 - 290 pàgines
...been proved that, ABCD being a parallelogram, AB will be = CD, and AD=BC. THEOREM XIII. PL. l.fig.3l All parallelograms on the same or equal bases and...same parallels are equal to one another ; that is, if BD=GH, and the lines BH and AF are parallel, then &e parallelogram ABDC—BDFE—EFHG. For AC=BD=EF... | |
 | Thomas Perronet Thompson - 1833 - 168 pàgines
...upon the same base, &c. Which was to be demonstrated. PROPOSITION XXXVIII. THEOREM. — Triangles upon equal bases, and between the same parallels, are equal to one another. Let the triangles ABC, DEF be upon c ADH equal bases BC, EF, and between the same parallels AD, BF.... | |
 | Francis Joseph Grund - 1834 - 202 pàgines
...equal to a rectangle upon the same basis, and of the same height. (Truth I.) 2dly. Parallelograms upon equal bases, and between the same parallels, are equal to one another ; for if they are between the same parallels, their heights must be equal. (Query 11, Sect. I.) 3dly.... | |
 | 1835 - 684 pàgines
...altitude . cor. 16 • From two Greek words, signifying " along one another.* (i) Parallelograms upon the same or equal bases, and between the same parallels, are equal to one another 16 (/.•) If a parallelogram and a triangle stand upon the same base, and between the same parallels,... | |
 | Euclid - 1835 - 540 pàgines
...to the triangle d 7. Ax. DBC. Wherefore, " triangles," &c. QED PROP. XXXVIII. THEOR. Triangles upon equal bases, and between the same parallels, are equal to one another. Let the triangles ABC, DEF be upon equal bases BC, EF, and between the same parallels BF, AD : The... | |
 | 1836 - 530 pàgines
...equal to two angles of the others, and the interjacent side equal, are equal in all respects. /, g Parallelograms on the same or equal bases, and between the same parallels, are equal. The explanation of this is as follows : the whole proposition is divided into distinct assertions,... | |
 | Robert Mudie - 1836 - 524 pàgines
...quantity. This, which is a very useful property, is usually cited in the words, " Parallelograms upon the same or equal bases, and between the same parallels, are equal to each other." But there is some objection to the words " between the same parallels," inasmuch as, to... | |
 | Robert Mudie - 1836 - 542 pàgines
...quantity. This, which is a very useful property, is usually cited in the words, " Parallelograms upon the same or equal bases, and between the same parallels, are equal to each other." But there is some objection to the words "between the same parallels," inasmuch as, to... | |
 | 1836 - 488 pàgines
...upon, the same base, and between the same parallels, are equal to one another. XXXVIII. Triangles upon equal bases, and between the same parallels, are equal to one another. XXXIX. Equal triangles upon the same base, and upon the same side of it, are between the same parallels.... | |
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Triangles upon equal bases, and between the same parallels, are equal to one another. 
