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" DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i. "
The First Six Books with Notes - Page 25
by Euclid - 1822 - 179 pages
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The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

Euclides - 1821
...the given triangles as halves they are .-. equal, PROP. 39, THEOR. Equal triangles on the same base and on the same side of it are between the same parallels, For if they are not, draw through the vertex of one of them a line par. to the base, it cuts a side of the...
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Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Euclid, Rev. John Allen - Astronomy - 1822 - 494 pages
...1], are also equal [Ax. 7]. PROP. XXXIX. THEOR. Equal triangles (ABC, DBC), on the same base (BC), and on the same side of it, are between the same parallels. Join AD, which is parallel to BC ; for, if not, through A, draw AE parallel to BC[31. 1], meeting either...
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A treatise on navigation, and nautical astronomy

Edward Riddle - Nautical astronomy - 1824 - 551 pages
...parallele, Cor. 2. Equal triangles, or equal parallelograms on equal bases, in the same straight line and on the same side of it are between the same parallels. THEOREM XXXVII. If any two parallelograms, AC, EG, have two sides AB, AD, and the contained angle BAD...
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The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 324 pages
...C. PROPOSITION XL. THEOREM. (173) Equal triangles (BAC and EDF) on equal bases and on the same side, are between the same parallels. For if the right line AD which joins the vertices of the two triangles be not parallel to BF, draw through ^ the point A the right line AG parallel to BF, /(~~~"...
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Dialogues on the First Principles of the Newtonian System, Volume 4

Walter Henry Burton - Astronomy - 1828 - 68 pages
...equal triangles Prop. xii. upon the same base (or upon equal bases in the same straight line) and upon the same side of it, are between the same parallels. For if the straight line which joins the vertices of the two triangles be not parallel to the base, some other...
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The First Six Books of the Elements of Euclid: With Notes

Euclid - Euclid's Elements - 1833 - 183 pages
...therefore _ * equal (4). PROP. XXXIX. THEOR. Equal triangles (BAC and BDC), on the same base Fig. 58. and on the same side of it, are between the same parallels. If the right line AD, which joins the vertices of the triangles, be not parallel to BC, draw through...
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Geometry Without Axioms; Or the First Book of Euclid's Elements. With ...

Thomas Perronet Thompson - Euclid's Elements - 1833 - 150 pages
...PROPOSITION XL. See Note. THEOREM. — Equal triangles, upon equal bases in ihe same straight line, and on the same side of it, are between the same parallels. Let the triangles ABC, EFD, which are upon equal bases BC and EF in the same straight line BF, and...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 390 pages
...38.) supplemental, the triangles are equal. PROB. XXXIX. THEOR.* EQUAL triangles upon the same base, and on the same side of it, are between the same parallels. Let the equal triangles ABC, DBC be on the same base BC, and on the same side of it ; they are between...
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840
...to AB. PROP. XL. THEOR. Equal triangles (ACB, DFE) on equal bases (AB, DE), in the same right line, and on the same side of it, are between the same parallels. For if it be supposed that CF joining the vertices of the equal triangles is not parallel to AE, but that...
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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840
...between the same parallels. PROP. XL. THEOR. Equal triangles on equal bases, in the same right line, and on the same side of it, are between the same parallels. PROP. XLI. THEOR. If a parallelogram and a triangle are upon the same base and between the same parallels,...
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