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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 Book of Euclid's Elements: Arranged for Beginners - Seite 135
von Euclid, John Bascombe Lock - 1892 - 167 Seiten
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The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

Euclides - 1821 - 294 Seiten
...formed of which 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...
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Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Rev. John Allen - 1822 - 516 Seiten
...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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The First Six Books with Notes

Euclid - 1822 - 222 Seiten
...therefore equal(4). (' " . PROP. XXXIX. THEOR. Equal triangles (BAC and BDC) on the same base Fig-ss. and on the same side of it are between the same parallels. For if the right line AD which joins the vertices of the triangles be not parallel to BC, draw through...
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A treatise on navigation, and nautical astronomy

Edward Riddle - 1824 - 572 Seiten
...part, can be parallel to AB, and DC is consequently parallel to A BQED Cor. 1. Equal parallelograms, on the same base, and on the same side of it, are between the same parallele, Cor. 2. Equal triangles, or equal parallelograms on equal bases, in the same straight line...
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The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - 1828 - 542 Seiten
...triangle into as many equal parts. PROPOSITION XXXIX. THEOREM. (172) Equal triangles (BAG and BDC) on the same base and on the same side of it are between the same parallels. For 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 - 1833 - 168 Seiten
...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 on the...
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The First Six Books of the Elements of Euclid: With Notes

Euclid - 1833 - 216 Seiten
...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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A System of Popular Geometry: Containing in a Few Lessons So Much of the ...

George Darley - 1836 - 172 Seiten
...triangles ABC, DBF, are also equal*. This, &c. ART. 27. Equal triangles upon the same base, andupon the same side of it, are between the same parallels. Let ABC, ADC, be two equal triangles on the same base AC, and on the same side of it. Then these triangles are...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - 410 Seiten
...angles (I. def. 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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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840 - 82 Seiten
...equal bases and between the same parallels, are equal. BDE PROP. XXXIX. THEOR. Equal triangles upon the same base and on the same side of it, are between the same parallels. PROP. XL. THEOR. Equal triangles on equal bases, in the same right line, and on the same side of it,...
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