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" Triangles upon equal bases, and between the same parallels, are equal to one another. "
A Treatise of Practical Surveying: Which is Demonstrated from Its First ... - Strona 43
autor: Robert Gibson - 1806 - Liczba stron: 452
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Popular Mathematics: Being the First Elements of Arithmetic, Algebra, and ...

Robert Mudie - 1836 - Liczba stron: 542
...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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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - Liczba stron: 488
...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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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - Liczba stron: 290
...therefore the triangle ABC is equal to the triangle DBC. PROPOSITION XXXVm. THEOREM. 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...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - Liczba stron: 410
...triangle ABC is equal to the triangle DBC. Wherefore triangles, &c. 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 : ABC...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838 - Liczba stron: 264
...EBCF. Therefore parallelograms upon the same base, &c. QED PROP. XXXVI. THEOR. Parallelograms upon equal bases, and between the same parallels, are equal to one another. Let ABCD, EFGH be parallelograms upon equal bases BC, F6 and between the same parallels AH, BG: the...
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The Theory and Practice of Surveying: Containing All the Instructions ...

Robert Gibson, James Ryan - 1839 - Liczba stron: 452
...proved that, ABCD being a parallelogram, AB will be = CD, and AD—BC. C THEOREM XIII. PL. 1. fig. 31 All parallelograms on the same or equal bases and...are equal to one another ; that is, if BD=GH, and tlie lines BH and AF arc parallel, then the parallelogram A11DC—BDFE—EFHG. For AC=BD=EF (by cor....
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Crocker's Elements of land surveying. To which are added, Tables of six ...

Abraham Crocker - 1841 - Liczba stron: 486
...will be the rhomboides. W For Practice. Note. Parallelograms constituted upon the same base (or on equal bases), and between the same parallels, are equal to one another. — EUCLID, I. 35. and 36. In every quadrilateral (or four-sided) figure, the four angles, taken together,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - Liczba stron: 332
...the parallelogram ABCD is equal to the parallelogram EBCF. PROP. XXXVI. THEOR. Parallelograms upon equal bases, and between the same parallels, are equal to one another. Let ABCD, EFGH be parallelograms upon equal bases BC, FG, and between the same parallels AH, BG ; the...
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Proceedings

Scotland free church, gen. assembly - 1847 - Liczba stron: 554
...and EFGH, being each of them equal to GCDH, are equal to one another. Wherefore, parallelograms upon equal bases, and between the same parallels, are equal to one another. 4. Let AB be divided into two parts in C,-any part, AB'=AC»+CD' + 2AC.CB. J Upon AB describe a square...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - Liczba stron: 546
...equal to the triangle DBC. Wherefore triangles, &c. «. ED PROPOSITION XXXVIII. THEOREM. 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 /,"/•', AD....
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