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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Resultater 1-5 af 92
Side 9
... base BC shall be equal to the base EF , and the triangle ABC to the tri- angle DEF , and the other angles shall be equal , each to each , to which the equal AA sides are opposite , namely , the angle ABC to the angle DEF , and the angle ...
... base BC shall be equal to the base EF , and the triangle ABC to the tri- angle DEF , and the other angles shall be equal , each to each , to which the equal AA sides are opposite , namely , the angle ABC to the angle DEF , and the angle ...
Side 10
... base BC will coincide with the base EF ; because , B coinciding with E and C with F , if the base BC does not coincide with the base EF , two straight lines will enclose a space ; which is impossible . [ Axiom 10 . Therefore the base BC ...
... base BC will coincide with the base EF ; because , B coinciding with E and C with F , if the base BC does not coincide with the base EF , two straight lines will enclose a space ; which is impossible . [ Axiom 10 . Therefore the base BC ...
Side 12
... BC is common to both , B [ I. 3 . [ Construction . the two sides DB , BC are equal to the two sides AC , CB , each to each ; and the angle DBC is equal to the angle ACB ; [ Hypothesis . therefore the base DC is equal to the base AB ...
... BC is common to both , B [ I. 3 . [ Construction . the two sides DB , BC are equal to the two sides AC , CB , each to each ; and the angle DBC is equal to the angle ACB ; [ Hypothesis . therefore the base DC is equal to the base AB ...
Side 13
... BC is equal to BD , the angle BDC is equal to the angle BCD . [ Hypothesis ... base CD , are equal to one another . [ I. 5 . But the angle ECD is greater ... BC is equal to BD , the angle BDC is equal to the angle BCD . [ Hypothesis . [ I ...
... BC is equal to BD , the angle BDC is equal to the angle BCD . [ Hypothesis ... base CD , are equal to one another . [ I. 5 . But the angle ECD is greater ... BC is equal to BD , the angle BDC is equal to the angle BCD . [ Hypothesis . [ I ...
Side 14
... BC is equal to EF . [ Hyp . Therefore , BC coinciding with EF , BA and AC will coin- cide with ED and DF . For if the base BC coincides with the base EF , but the sides BA , CA do not coincide with the sides ED , FD , but have a ...
... BC is equal to EF . [ Hyp . Therefore , BC coinciding with EF , BA and AC will coin- cide with ED and DF . For if the base BC coincides with the base EF , but the sides BA , CA do not coincide with the sides ED , FD , but have a ...
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Almindelige termer og sætninger
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.