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 páginas |
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Página 9
... bases or third sides equal ; and the two triangles shall be equal , and their other angles shall be equal , each to ... BC shall be equal to the base EF , and the triangle ABC to the tri- angle DEF , and the other angles shall be equal ...
... bases or third sides equal ; and the two triangles shall be equal , and their other angles shall be equal , each to ... BC shall be equal to the base EF , and the triangle ABC to the tri- angle DEF , and the other angles shall be equal ...
Página 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 ...
Página 12
... BC is common to both , B A LI . 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 A LI . 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 ...
Página 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 ...
Página 14
... base BC equal to the base EF : the angle BÁC shall be equal to the angle EDF . D B E For if the triangle ABC be applied to the triangle DEF , so that the point B may be on the point E , and the straight line BC on the straight line EF ...
... base BC equal to the base EF : the angle BÁC shall be equal to the angle EDF . D B E For if the triangle ABC be applied to the triangle DEF , so that the point B may be on the point E , and the straight line BC on the straight line EF ...
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Términos y frases comunes
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