The Elements of Euclid for the Use of Schools and Colleges: Comprising the First Six Books and Portions of the Eleventh and Twelfth Books : with Notes, an Appendix, and ExercisesMacmillan, 1867 - 400 sider |
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Side 35
... parallel to BC . [ Construction . [ I. 27 . Wherefore the straight line EAF is drawn through the given point A , parallel to the given straight line BC . Q.E.F. XVIII PROPOSITION 32. THEOREM . If a side of any triangle be produced , the ...
... parallel to BC . [ Construction . [ I. 27 . Wherefore the straight line EAF is drawn through the given point A , parallel to the given straight line BC . Q.E.F. XVIII PROPOSITION 32. THEOREM . If a side of any triangle be produced , the ...
Side 37
... parallel . Let AB and CD be equal and parallel straight lines , and let them be joined towards the same parts by the straight lines AC and BD : AC and BD shall be equal and parallel . Join BC . Then because AB is par- allel to CD ...
... parallel . Let AB and CD be equal and parallel straight lines , and let them be joined towards the same parts by the straight lines AC and BD : AC and BD shall be equal and parallel . Join BC . Then because AB is par- allel to CD ...
Side 38
... parallel to CD , and BC meets them , the alternate angles ABC , BCD are equal to one an- other . [ I. 29 . B And because AC is parallel to BD , and BC meets them , the alternate angles ACB , CBD are equal to one another . [ I. 29 ...
... parallel to CD , and BC meets them , the alternate angles ABC , BCD are equal to one an- other . [ I. 29 . B And because AC is parallel to BD , and BC meets them , the alternate angles ACB , CBD are equal to one another . [ I. 29 ...
Side 40
... parallel . Therefore BE , CH are both equal and parallel . Therefore EBCH is a parallelogram . [ I. 33 . [ Definition . And it is equal to ABCD , because they are on the same base BC , and between the same parallels BC , AH . [ I. 35 ...
... parallel . Therefore BE , CH are both equal and parallel . Therefore EBCH is a parallelogram . [ I. 33 . [ Definition . And it is equal to ABCD , because they are on the same base BC , and between the same parallels BC , AH . [ I. 35 ...
Side 41
... parallels BF , AD : the triangle ABC shall be equal to the triangle DEF . Produce AD both ways to the points H G , H ; through B draw BG parallel to CA , and through F draw FH parallel to ED . [ I. 31 . B Then each of the figures GBCA ...
... parallels BF , AD : the triangle ABC shall be equal to the triangle DEF . Produce AD both ways to the points H G , H ; through B draw BG parallel to CA , and through F draw FH parallel to ED . [ I. 31 . B Then each of the figures GBCA ...
Andre utgaver - Vis alle
The Elements of Euclid for the Use of Schools and Colleges Isaac Todhunter Uten tilgangsbegrensning - 1872 |
The Elements of Euclid for the Use of Schools and Colleges: Comprising the ... Euclid,Isaac Todhunter Uten tilgangsbegrensning - 1884 |
The Elements of Euclid for the Use of Schools and Colleges: Comprising the ... Euclid,Isaac Todhunter Uten tilgangsbegrensning - 1867 |
Vanlige uttrykk og setninger
ABCD AC is equal angle ABC angle ACB angle BAC angle EDF angles equal Axiom base BC bisects the angle centre chord circle ABC circle described circumference Construction Corollary describe a circle diameter double draw a straight equal angles equal to F equiangular equilateral equimultiples Euclid Euclid's Elements exterior angle given circle given point given straight line gnomon Hypothesis inscribed intersect isosceles triangle less Let ABC magnitudes middle point multiple opposite angles opposite sides parallelogram perpendicular plane polygon produced proportionals PROPOSITION 13 Q.E.D. PROPOSITION quadrilateral rectangle contained rectilineal figure remaining angle rhombus right angles right-angled triangle segment shew shewn side BC square on AC straight line &c straight line drawn tangent THEOREM touches the circle triangle ABC triangle DEF twice the rectangle vertex Wherefore
Populære avsnitt
Side 35 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.
Side 67 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle, is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse angle, Let ABC be an obtuse-angled triangle, having the obtuse angle...
Side 73 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a Right Angle; and the straight line which stands on the other is called a Perpendicular to it.
Side 284 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 50 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Side 57 - If a straight line be divided into two equal parts, and also into two unequal parts ; the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Side 10 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Side 227 - If two straight lines be at right angles to the same plane, they shall be parallel to one another. Let the straight lines AB, CD be at right angles to the same plane : AB is parallel to CD.
Side 102 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Side 352 - Prove that the square on any straight line drawn from the vertex of an isosceles triangle to the base, is less than the square on a side of the triangle by the rectangle contained by the segments of the base : and conversely.