The Elements of Euclid for the Use of Schools and CollegesMacmillan, 1872 - 400 Seiten |
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Seite 9
... equal to C the less . From the point A draw the straight line AD equal to C ; [ I. 2 . and from the centre A , at ... angles contained by those sides equal to one another , they shall also have their bases or third sides equal ; and the ...
... equal to C the less . From the point A draw the straight line AD equal to C ; [ I. 2 . and from the centre A , at ... angles contained by those sides equal to one another , they shall also have their bases or third sides equal ; and the ...
Seite 10
... equal to DE . And , AB coinciding with DE , AC will fall on DF , because the angle BAC is equal to the angle EDF . B ... angles of the one coincide with the other angles of the other , and are equal to them , namely , the angle ABC to ...
... equal to DE . And , AB coinciding with DE , AC will fall on DF , because the angle BAC is equal to the angle EDF . B ... angles of the one coincide with the other angles of the other , and are equal to them , namely , the angle ABC to ...
Seite 11
... equal to the two sides GA , AB , each to each ; and they contain the angle FAG common to the two triangles AFC , AGB ; therefore the base FC is equal to the base GB , and the triangle AFC to the triangle AGB , and the remaining angles ...
... equal to the two sides GA , AB , each to each ; and they contain the angle FAG common to the two triangles AFC , AGB ; therefore the base FC is equal to the base GB , and the triangle AFC to the triangle AGB , and the remaining angles ...
Seite 12
... equal angles , shall be equal to one another . Let 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 ...
... equal angles , shall be equal to one another . Let 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 ...
Seite 13
... equal to one another . Join CD . In the case in which the vertex of each tri- angle is without the other triangle ... angles ECD , FDC , on the other side of the base CD , are equal to one another . [ I. 5 . But the angle ECD is greater ...
... equal to one another . Join CD . In the case in which the vertex of each tri- angle is without the other triangle ... angles ECD , FDC , on the other side of the base CD , are equal to one another . [ I. 5 . But the angle ECD is greater ...
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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