| Euclides - 1860
...and triangles, having equal bases, are to one another as their altitudes. PROPOSITION II. THEOBEM. **If a straight line be drawn parallel to one of the...sides of a triangle, it shall cut the other sides, or** the other sides produced ^proportionally ; and if the sides, or the sides produced, be cut proportionally,... | |
| War office - 1861
...two straight lines shall be parallel. 8. Draw a tangent to a circle from a given point without it. 9. **If a straight line be drawn parallel to one of the...the other sides or those produced proportionally.** How must a line be drawn parallel to the base of a triangle, so as to be equal to half the base. 10.... | |
| War office - 1861 - 12 sider
...angle. VOLUNTARY PORTION. 1. Inscribe an equiangular and equilateral pentagon in a given circle. 2. **If a straight line be drawn parallel to one of the...sides of a triangle, it shall cut the other sides or** these produced proportionally ; and if the sides or the sides produced be cut proportionally, the straight... | |
| Euclides - 1861
...3, I. 2 C. D. 1 H. 2 C. 1,&26,L 3 Ax. 2, I, C. & 1, VI. Ax. 1, I. 4 5 PROP. 2. — THEOR. If a st. **line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or** these produced, proportionally ; and conversely, if the sides, or sides produced, be cut proportionally,... | |
| Woolwich roy. military acad - 1861
...circle be respectively parallel to their opposite sides, the remaining sides are parallel to each other. **straight line which joins the points of section shall...be parallel to the remaining side of the triangle.** If two triangles be on equal bases and between the same parallels, shew that the sides of the triangles... | |
| Euclides - 1864
...construction be made as in the proposition, the demonstration will be the same. PROPOSITION n. THEOREM. **If a, straight line be drawn parallel to one of the...sides of a triangle, it shall cut the other sides, or** these produced, proportionally : and conversely, if the sides, or the sides produced, be cut proportionally,... | |
| J. F. H. de Rheims - 1865 - 169 sider
...segment less than a semicircle is greater than a right angle. EUCLID, BOOK VI. Prop. 2. — Theorem. **If a straight line be drawn parallel to one of the...sides or those produced proportionally, and if the** side or the sides produced be cut proportionally, the straight line which joins the points of section... | |
| 1865
...triangle having each of the angles at the base double of the third angle. Book VI. Proposition 2. Theorem. **If a straight line be drawn parallel to one of the...sides of a triangle, it shall cut the other sides, or** these produced proportionally ; and conversely, if the sides, or the sides produced, be cut proportionally,... | |
| Euclides - 1865
...construction be made as in the proposition, the demonstration will be the same. PROP. H.— THEOREM. **If a straight line be drawn parallel to one of the sides of a triangle, it shall** out the other sides, on these produced, proportionally; and conversely, if the sides, or the sides... | |
| James Robert Christie - 1866 - 404 sider
...angle in a semicircle is a right angle; but the angle in a segment greater than a semicircle is &c. 4. **If a straight line be drawn parallel to one of the...sides of a triangle, it shall cut the other sides, or** these produced, proportionally : and, conversely, if the sides &c. 5. If two straight lines meeting... | |
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