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 4
... triangle is that which has three unequal sides : 27. A right - angled triangle is that which has a right angle : [ The side opposite to the right angle in a right - angled triangle is fre- quently called the hypotenuse . ] 28. An obtuse ...
... triangle is that which has three unequal sides : 27. A right - angled triangle is that which has a right angle : [ The side opposite to the right angle in a right - angled triangle is fre- quently called the hypotenuse . ] 28. An obtuse ...
Side 16
... triangle DFE , and join CF. [ I. 1 . The straight line CF drawn from the given point C shall be at right angles to the given straight line AB . Because DC is equal to CE , [ Construction . and CF is common to the two triangles DCF , ECF ...
... triangle DFE , and join CF. [ I. 1 . The straight line CF drawn from the given point C shall be at right angles to the given straight line AB . Because DC is equal to CE , [ Construction . and CF is common to the two triangles DCF , ECF ...
Side 20
... right angles . A [ I. 13 . Again , because the straight line DE makes with ... triangle be produced , the exterior angle shall be greater than either of ... angle AEB is equal to the angle CEF 20 EUCLID'S ELEMENTS .
... right angles . A [ I. 13 . Again , because the straight line DE makes with ... triangle be produced , the exterior angle shall be greater than either of ... angle AEB is equal to the angle CEF 20 EUCLID'S ELEMENTS .
Side 21
... angle BCG , that is the angle ACD , is greater than the angle ABC . [ I. 15 . Wherefore , if one side & c . Q.E.D. PROPOSITION 17. THEOREM . Any two angles of a triangle are together less than two right angles . Let ABC be a triangle ...
... angle BCG , that is the angle ACD , is greater than the angle ABC . [ I. 15 . Wherefore , if one side & c . Q.E.D. PROPOSITION 17. THEOREM . Any two angles of a triangle are together less than two right angles . Let ABC be a triangle ...
Side 35
... triangle be produced , the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are toge- ther equal to two right angles . Let ABC be a triangle , and let one of its sides BC ...
... triangle be produced , the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are toge- ther equal to two right angles . Let ABC be a triangle , and let one of its sides BC ...
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ABCD angle ABC angle ACB angle BAC angle EDF angles equal Axiom base BC BC is equal 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 radius 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
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Side 286 - 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 30 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Side 34 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon the same side; and likewise the two interior angles upon the same side together equal to two right angles...
Side 37 - 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 together equal to two right angles.
Side 12 - 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 302 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.
Side 220 - If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Side 354 - 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.
Side 104 - 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 96 - The opposite angles of any quadrilateral figure inscribed in a circle, are together equal to two right angles.