 | 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 the... | |
 | 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... | |
 | 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... | |
 | 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 the... | |
 | Walter Henry Burton - 1828 - 84 Seiten
...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... | |
 | 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... | |
 | 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... | |
 | Euclid, James Thomson - 1837 - 410 Seiten
...a point in which the circumferences meet, the circles must touch one another in that point. IF two triangles on the same base, and on the same side of it, have equal vertical angles, the vertex of each is in the circumference of the circle described about... | |
 | 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,... | |
 | Euclides - 1840 - 192 Seiten
...therefore be also greater than Z. BDC, of which however it is but a part ; which is absurd. Therefore, two triangles on the same base, and on the same side of it, cannot have their conterminous sides equal at both extremities of the base, when the vertex of the... | |
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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. 
