 | Francis Joseph Grund - 1830 - Liczba stron: 274
...the magnitude of an angle does not depend upon the greatneii 12* 128 GEOMETRY. 5. Parallelograms upon equal bases and between the same parallels are equal to one another. 6. The area of a parallelogram is found by multiplying the basis given in rods, feet inches, &c. by... | |
 | Augustus De Morgan - 1831 - Liczba stron: 108
...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 - Liczba stron: 290
...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...another ; that is, if BD=GH, and the lines BH and AF are parallel, then &e parallelogram ABDC—BDFE—EFHG. For AC=BD=EF (by cor. the last) ; to both add... | |
 | Robert Gibson - 1833 - Liczba stron: 436
...AD=BC. THEOREM XIII. PL. i;fig. 31 All parallelogram on the same or equal bases and between the samt parallels are equal to one another ; that is, if BD=GH, and the lines Bit and AF are parallel, then the parallelogram ABDC—BDFE—EFHG. For AC=BD=EF (by cor. the last)... | |
 | Thomas Perronet Thompson - 1833 - Liczba stron: 168
...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 - Liczba stron: 202
...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 - Liczba stron: 684
...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 - Liczba stron: 540
...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 - Liczba stron: 530
...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 - Liczba stron: 524
...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... | |
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Triangles upon equal bases, and between the same parallels, are equal to one another. 
