The Elements of Euclid for the Use of Schools and Colleges: Comprising the First Six Books and Portions of the Eleventh and Twelfth BooksMacmillan, 1886 - 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 . 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 . 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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Häufige Begriffe und Wortgruppen
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