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" Equal triangles on the same base, and on the same side of it, are between the same parallels. "
Euclid's Elements of Geometry: The Six First Books. To which are Added ... - Σελίδα 47
των Rev. John Allen - 1822 - 494 σελίδες
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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...

The First Six Books with Notes

Euclid - 1822 - 179 σελίδες
...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...

A treatise on navigation, and nautical astronomy

Edward Riddle - 1824 - 551 σελίδες
...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...

The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - 1828 - 324 σελίδες
...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...

The first six books of the Elements of Euclid: with notes

Euclid, Thomas Elrington - 1833 - 183 σελίδες
...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...

Geometry Without Axioms; Or the First Book of Euclid's Elements. With ...

Thomas Perronet Thompson - 1833 - 150 σελίδες
...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...

Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1837 - 318 σελίδες
...ABC is equal to the triangle DEF. PROP. XXXIX. THEOR. Equal triangles upon the same base, and upon the same side of it, are between the same parallels. Join AD ; AD is parallel to BC ; for, if it is not, through the point A draw (31. K) AE parallel to BC, and...

The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - 1837 - 390 σελίδες
...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 the same parallels. Join AD ; AD is parallel to BC. For, if it be not, through A...

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...

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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