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 σελίδες |
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Σελίδα 18
... PROPOSITION 13 . THEOREM . The angles which one straight line makes with another straight line on one side of it , either are two right angles , or are together ... Q.E.D. PROPOSITION 14 . THEOREM . If , at a point 18 EUCLID'S ELEMENTS .
... PROPOSITION 13 . THEOREM . The angles which one straight line makes with another straight line on one side of it , either are two right angles , or are together ... Q.E.D. PROPOSITION 14 . THEOREM . If , at a point 18 EUCLID'S ELEMENTS .
Σελίδα 19
... PROPOSITION 14 . THEOREM . If , at a point in a straight line , two other straight lines , on the opposite sides of ... Q.E.D. PROPOSITION 15. THEOREM . If two straight lines cut one another , the vertical , or opposite , angles shall be ...
... PROPOSITION 14 . THEOREM . If , at a point in a straight line , two other straight lines , on the opposite sides of ... Q.E.D. PROPOSITION 15. THEOREM . If two straight lines cut one another , the vertical , or opposite , angles shall be ...
Σελίδα 21
... Q.E.D. PROPOSITION 17. THEOREM . Any two angles of a triangle are together less than two right angles . Let ABC be a triangle : any two of its angles are together less than two right angles . Produce BC to D. Then because ACD is the ...
... Q.E.D. PROPOSITION 17. THEOREM . Any two angles of a triangle are together less than two right angles . Let ABC be a triangle : any two of its angles are together less than two right angles . Produce BC to D. Then because ACD is the ...
Σελίδα 22
... Q.E.D. PROPOSITION 19. THEOREM . [ Axiom 9 . The greater angle of every triangle is subtended by the greater side , or has the greater side opposite to it . Let ABC be a triangle , of which the angle ABC is greater than the angle ACB ...
... Q.E.D. PROPOSITION 19. THEOREM . [ Axiom 9 . The greater angle of every triangle is subtended by the greater side , or has the greater side opposite to it . Let ABC be a triangle , of which the angle ABC is greater than the angle ACB ...
Σελίδα 23
... Q.E.D. PROPOSITION 20 . THEOREM . Any two sides of a triangle are together greater than the third side . Let ABC be a triangle : any two sides of it are together greater than the third side ; namely , BA , AC greater than BC ; and AB ...
... Q.E.D. PROPOSITION 20 . THEOREM . Any two sides of a triangle are together greater than the third side . Let ABC be a triangle : any two sides of it are together greater than the third side ; namely , BA , AC greater than BC ; and AB ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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...
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 302 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 96 - The opposite angles of any quadrilateral figure inscribed in a circle, are together equal to two right angles.