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" Let ABCD, ABEF, be two parallelograms, and ABC, ABF, two triangles, standing on the same base AB, and between the same parallels AB, DE ; then will the parallelogram ABCD be equal to the parallelogram ABEF, and the triangle ABC equal to the triangle ABF. "
The Mechanic's Calculator: Comprehending Principles, Rules, and Tables in ... - Page 56
by William Grier - 1836 - 344 pages
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A Course of Mathematics ...: Composed for the Use of the Royal Military ...

Charles Hutton - Mathematics - 1811 - 406 pages
...Triangle, or the Triangle Half the Parallelogram. Let ABCD be a parallelogram, and ABE a triangle, on the same base AB, and between the same parallels AB, DE ; then will the parallelogram ABCD be double the triangle ABE, or the triangle half the parallelogram. For, draw the diagonal AC of the parallelogram,...
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A Course of Mathematics: For the Use of Academies as Well as Private Tuition

Charles Hutton - Mathematics - 1812 - 620 pages
...Same Parallels, are equal to each other. Let E Let ABCD, ABEP, be two parallelograms, and ABC, ABF, two triangles, standing on the same base AB, and between...same parallels AB, DE; then will the parallelogram A BCD, be equal tor the parallelogram ABEF, and the triangle ABC equal to the triangle ABF. For, since...
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A Course of Mathematics: In Two Volumes : for the Use of Academies ..., Volume 1

Charles Hutton - Mathematics - 1816 - 610 pages
...Triangle, or the Triangle Half the Parallelogram. Let ABCD be a parallelogram, and ABE, a triangle, on uc same base AB, and between the same parallels AB, DE ; then will the parallelogram AB(D be double the triangle ABE, or the trhngle half the parallelogram. For, draw tie diagonal AC of...
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A Course of Mathematics: In Two Volumes. For the Use of Academies ..., Volume 1

Charles Hutton - Arithmetic - 1818 - 646 pages
...Parallels, are equal to each ether. Let Let ABCD, ABEF, be two parallelo- 3> CF 3S grams, and ABC, ABF, two triangles, standing on the same base AB, and between...ABEF, and the triangle ABC equal to the triangle ABF. For, since the line DE cuts the two parallels AF, BE, and the two AD, sc, it makes the angle E equal...
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A Course of Mathematics: For the Use of Academies, as Well as Private ...

Charles Hutton - Mathematics - 1822 - 616 pages
...Same Parallels, are equal to each other. Let £98 Let ABCD, ABEF, be two parallelograms, and ABC, ABF, two triangles, standing on the same base AB, and between...parallelogram ABEF, and the triangle ABC equal to the triangle ARP. For, since the line DE cuts the two parallels AF, BE, and the two AD, BC, it makes the angle K...
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A Course of Mathematics for the Use of Academies: As Well as ..., Volume 1

Charles Hutton - Mathematics - 1825 - 608 pages
...halves of the said equal parallelograms (th '_'*) o.. E D. C'irol. 1. Parallelograms, or triangle!', having the same base and altitude, are equal For the...perpendicular or distance between the two parallels, which is every where equal, by the definition of parallels Carol 2. Parallelograms, or triangle*, having equal...
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Mechanics Magazine, Volume 4

Industrial arts - 1825 - 546 pages
...draw AF parallel to BL), of the triangle ABU; then we shrill have two parallelograms, AliCK and ABDF, standing on the same base, AB, and between the same parallels, AB and CD; then (by Cor. 3. of the last Theorem) these parallelograms are equal to each other ; but the...
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Mechanics' Magazine and Journal of Science, Arts, and Manufactures, Volume 4

Industrial arts - 1825 - 484 pages
...draw AF parallel to BD, of the triangle ABI); then we shall have two parallelograms, ABCK and AUDI', standing on the same base, AB, and between the same parallels, AB and CD; then (by Cor. '2. of the last Theorem) these parallelograms are equal to each other ; but the...
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Iron: An Illustrated Weekly Journal for Iron and Steel ..., Volume 4

Perry Fairfax Nursey - Industrial arts - 1825 - 476 pages
...Л !•' parallel to BD, of the triangle ABI); then we shall have two parallelograms, ABUE and ABDF. standing on the same base, AB, and between the same parallels, AB and CD; then (by Cor. 2. of the last Theorem) these parallelograms are equal to each other; but the...
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A Course of Mathematics: For the Use of Academies as Well as ..., Volume 1

Charles Hutton - Mathematics - 1831 - 632 pages
...triangle, or the triangle half the parallelogram. Let ABCD be the parallelogram, and ABE a triangle, on the same base AB, and between the same parallels AB, DE ; then will the parallelogram ABCD be double the triangle ABE, or the triangle half the parallelogram. J> A For, draw the diagonal AC of...
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