The Elements of Euclid for the Use of Schools and CollegesMacmillan, 1872 - 400 Seiten |
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Seite 9
... namely those to which the equal sides are opposite . Let 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 ...
... namely those to which the equal sides are opposite . Let 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 ...
Seite 10
... namely , the angle ABC to the angle DEF , and the angle ACB to the angle DFE . Wherefore , if two triangles & c . Q.E.D. PROPOSITION 5. THEOREM . The angles at the base of an isosceles triangle are equal to one another ; and if the ...
... namely , the angle ABC to the angle DEF , and the angle ACB to the angle DFE . Wherefore , if two triangles & c . Q.E.D. PROPOSITION 5. THEOREM . The angles at the base of an isosceles triangle are equal to one another ; and if the ...
Seite 11
... namely the angle ACF to the angle ABG , and the angle AFC to the angle AGB . [ I. 4 . And because the whole AF is equal to the whole AG , of which the parts AB , AC are equal , [ Hypothesis . the remainder BF is equal to the remainder ...
... namely the angle ACF to the angle ABG , and the angle AFC to the angle AGB . [ I. 4 . And because the whole AF is equal to the whole AG , of which the parts AB , AC are equal , [ Hypothesis . the remainder BF is equal to the remainder ...
Seite 14
... namely AB to DE , and AC to DF , and also the base BC equal to the base EF : the angle BAC shall be equal to the angle EDF . A D G B E For if the triangle ABC be applied to the triangle DEF , so that the point B may be on the point E ...
... namely AB to DE , and AC to DF , and also the base BC equal to the base EF : the angle BAC shall be equal to the angle EDF . A D G B E For if the triangle ABC be applied to the triangle DEF , so that the point B may be on the point E ...
Seite 23
... namely , BA , AC greater than BC ; and AB , BC greater than AC ; and BC , CA greater than AB . Produce BA to D , making AD equal to AC , and join DC . B [ I. 3 . [ Construction . [ I. 5 . Then , because AD is equal to AC , the angle ADC ...
... namely , BA , AC greater than BC ; and AB , BC greater than AC ; and BC , CA greater than AB . Produce BA to D , making AD equal to AC , and join DC . B [ I. 3 . [ Construction . [ I. 5 . Then , because AD is equal to AC , the angle ADC ...
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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