The Elements of Euclid for the Use of Schools and Colleges: With Notes, an Appendix, and Exercises. comprising the first six books and portions of the eleventh and twelfth booksMacmillan and Company, 1880 - 400 Seiten |
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Seite 7
... triangle on a given finite straight line . Let AB be the given straight line : it is required to describe an ... ABC shall be an equilateral triangle . Tom Because the point A is the centre of the circle BCD , AC is equal to AB ...
... triangle on a given finite straight line . Let AB be the given straight line : it is required to describe an ... ABC shall be an equilateral triangle . Tom Because the point A is the centre of the circle BCD , AC is equal to AB ...
Seite 9
... ABC , DEF be two triangles which have the two sides AB , AC equal to the two sides DE , DF , each to each , namely , AB to DE , and AC to DF , and the angle BAC equal to the angle ... triangle ABC be applied to the triangle BOOK I. 3 , 4 . 9.
... ABC , DEF be two triangles which have the two sides AB , AC equal to the two sides DE , DF , each to each , namely , AB to DE , and AC to DF , and the angle BAC equal to the angle ... triangle ABC be applied to the triangle BOOK I. 3 , 4 . 9.
Seite 10
... ABC be applied to the triangle DEF , so that the point A may be on the point D , and the straight line AB on the ... triangle ABC coincides with the whole triangle DEF , and is equal to it . [ Axiom 8 . And the other angles of the one ...
... ABC be applied to the triangle DEF , so that the point A may be on the point D , and the straight line AB on the ... triangle ABC coincides with the whole triangle DEF , and is equal to it . [ Axiom 8 . And the other angles of the one ...
Seite 11
... ABC is equal to the remain- ing angle ACB , which are the angles at the base of the triangle ABC . [ Axiom 3 . And it has also been shewn that the angle FBC is equal to the angle GCB , which are the angles on the other side of the base ...
... ABC is equal to the remain- ing angle ACB , which are the angles at the base of the triangle ABC . [ Axiom 3 . And it has also been shewn that the angle FBC is equal to the angle GCB , which are the angles on the other side of the base ...
Seite 12
... ABC be a triangle , having the angle ABC equal to the angle ACB : the side AC shall be equal to the side AB . For if AC be not equal to AB , one of them must be greater than the other . Let AB be the greater , and from it cut off DB ...
... ABC be a triangle , having the angle ABC equal to the angle ACB : the side AC shall be equal to the side AB . For if AC be not equal to AB , one of them must be greater than the other . Let AB be the greater , and from it cut off DB ...
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ... Issac Todhunter Keine Leseprobe verfügbar - 2014 |
Häufige Begriffe und Wortgruppen
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 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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Seite 225 - 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.
Seite 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.
Seite 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.
Seite 39 - Triangles upon the same base, and between the same parallels, are equal to one another.
Seite 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.
Seite 353 - AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part.
Seite 67 - ... 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 ACB; and from the point A, let AD be drawn perpendicular to BC produced.
Seite 300 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.
Seite xv - PROPOSITION I. PROBLEM. To describe an equilateral triangle upon a given Jinite straight line. Let AB be the given straight line. It is required to describe an equilateral triangle upon AB, From the centre A, at the distance AB, describe the circle BCD ; (post.
Seite 36 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.