The Elements of Euclid for the Use of Schools and CollegesMacmillan, 1872 - 400 Seiten |
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Seite 8
... equal to a given straight line . Let A be the given point , and BC the given straight line it is required to draw from the point A a straight line equal to BC . From the point A to B draw the straight line AB ; [ Post . 1 . and on it ...
... equal to a given straight line . Let A be the given point , and BC the given straight line it is required to draw from the point A a straight line equal to BC . From the point A to B draw the straight line AB ; [ Post . 1 . and on it ...
Seite 10
... equal to DF . [ Hypothesis . But the point B was shewn to coincide with the point E , therefore the 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 ...
... equal to DF . [ Hypothesis . But the point B was shewn to coincide with the point E , therefore the 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 ...
Seite 12
... equal to AC the less , and join DC . Then , because in the triangles DBC , ACB , DB is equal to AC , and BC is common to both , B LI . 3 . [ Construction . the two sides DB , BC are equal to the two sides AC , CB , each to each ; and ...
... equal to AC the less , and join DC . Then , because in the triangles DBC , ACB , DB is equal to AC , and BC is common to both , B LI . 3 . [ Construction . the two sides DB , BC are equal to the two sides AC , CB , each to each ; and ...
Seite 14
... equal to the two sides DE , DF , each to each , 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 ...
... equal to the two sides DE , DF , each to each , 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 ...
Seite 23
... 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 is equal to the angle ACD ...
... 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 is equal to the angle ACD ...
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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