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
... CA , AB , BC are equal to one another . Wherefore the triangle ABC is equilateral , and it is described on the given straight line AB . [ Axiom 1 . [ Def . 24 . Q.E.F. PROPOSITION 2. PROBLEM . From a given point to draw.
... CA , AB , BC are equal to one another . Wherefore the triangle ABC is equilateral , and it is described on the given straight line AB . [ Axiom 1 . [ Def . 24 . Q.E.F. PROPOSITION 2. PROBLEM . From a given point to draw.
Seite 8
... Axiom 3 . But it has been shewn that BC is equal to BG ; therefore AL and BC are each of them equal to BG . But things which are equal to the same thing are equal to one another . [ Axiom 1 . Therefore AL is equal to BC . Wherefore from ...
... Axiom 3 . But it has been shewn that BC is equal to BG ; therefore AL and BC are each of them equal to BG . But things which are equal to the same thing are equal to one another . [ Axiom 1 . Therefore AL is equal to BC . Wherefore from ...
Seite 9
... Axiom 1 . Wherefore from AB the greater of two given straight lines a part AE has been cut off equal to C the less . Q.E.F. PROPOSITION 4 . THEOREM . If two triangles have two sides of the one equal to two sides of the other , each to ...
... Axiom 1 . Wherefore from AB the greater of two given straight lines a part AE has been cut off equal to C the less . Q.E.F. PROPOSITION 4 . THEOREM . If two triangles have two sides of the one equal to two sides of the other , each to ...
Seite 10
... Axiom 10 . Therefore the base BC coincides with the base EF , and is equal to it . [ Axiom 8 . Therefore the whole triangle ABC coincides with the whole triangle DEF , and is equal to it . [ Axiom 8 . And the other angles of the one ...
... Axiom 10 . Therefore the base BC coincides with the base EF , and is equal to it . [ Axiom 8 . Therefore the whole triangle ABC coincides with the whole triangle DEF , and is equal to it . [ Axiom 8 . And the other angles of the one ...
Seite 11
... Axiom 3 . And FC was shewn to be equal to GB ; therefore the two sides BF , FC are equal to the two sides CG , GB , each to each ; and the angle BFC was shewn to be equal to the angle CGB ; therefore the triangles BFC , CGB are equal ...
... Axiom 3 . And FC was shewn to be equal to GB ; therefore the two sides BF , FC are equal to the two sides CG , GB , each to each ; and the angle BFC was shewn to be equal to the angle CGB ; therefore the triangles BFC , CGB are equal ...
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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