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 11
... remaining angles of the one to the remaining angles of the other , each to each , to D which the equal sides are opposite , G namely the angle ACF to the angle ABG , and the angle AFC to the angle AGB . [ I. 4 . And because the whole AF ...
... remaining angles of the one to the remaining angles of the other , each to each , to D which the equal sides are opposite , G namely the angle ACF to the angle ABG , and the angle AFC to the angle AGB . [ I. 4 . And because the whole AF ...
Seite 19
... remaining angle ABE is equal to the remain- ing angle ABD , [ Axiom 3 . the less to the greater ; which is impossible . Therefore BE is not in the same straight line with CB . And in the same manner it may be shewn that no other can be ...
... remaining angle ABE is equal to the remain- ing angle ABD , [ Axiom 3 . the less to the greater ; which is impossible . Therefore BE is not in the same straight line with CB . And in the same manner it may be shewn that no other can be ...
Seite 20
... remaining angle CEA is equal to the re- maining angle DEB . [ Axiom 3 . In the same manner it may be shewn that the angle CEB is equal to the angle AED . Wherefore , if two straight lines & c . Q.E.D. Corollary 1. From this it is ...
... remaining angle CEA is equal to the re- maining angle DEB . [ Axiom 3 . In the same manner it may be shewn that the angle CEB is equal to the angle AED . Wherefore , if two straight lines & c . Q.E.D. Corollary 1. From this it is ...
Seite 21
... remaining angles to the remaining angles , each to each , to which the equal sides are opposite ; [ I. 4 . therefore the angle BAE is equal to the angle ECF . But the angle ECD is greater than the angle ECF . [ Axiom 9 . Therefore the ...
... remaining angles to the remaining angles , each to each , to which the equal sides are opposite ; [ I. 4 . therefore the angle BAE is equal to the angle ECF . But the angle ECD is greater than the angle ECF . [ Axiom 9 . Therefore the ...
Seite 32
... remaining angle AGH is equal to the remaining angle GHD ; [ Axiom 3 . and they are alternate angles ; therefore AB is parallel to CD . Wherefore , if a straight line & c . Q.E.D. [ I. 27 . PROPOSITION 29. THEOREM . If a straight line ...
... remaining angle AGH is equal to the remaining angle GHD ; [ Axiom 3 . and they are alternate angles ; therefore AB is parallel to CD . Wherefore , if a straight line & c . Q.E.D. [ I. 27 . PROPOSITION 29. THEOREM . If a straight line ...
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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