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 xvi
... hypothesis is used in the same sense as supposition . To assist the student in following the steps of the reasoning , references are given to the results already ob- tained which are required in the demonstration . Thus I. 5 indicates ...
... hypothesis is used in the same sense as supposition . To assist the student in following the steps of the reasoning , references are given to the results already ob- tained which are required in the demonstration . Thus I. 5 indicates ...
Seite 10
... Hypothesis . Therefore also the point C will coincide with the point F , because AC is 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 ...
... Hypothesis . Therefore also the point C will coincide with the point F , because AC is 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 ...
Seite 11
... Hypothesis . and AB to AC , the two sides FA , AC are 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 ...
... Hypothesis . and AB to AC , the two sides FA , AC are 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 ...
Seite 13
... Hypothesis . the angle ACD is equal to the angle ADC . [ I. 5 . But the angle ACD is greater than the angle BCD , [ Ax . 9 . therefore the angle ADC is also greater than the angle BCD ; much more then is the angle BDC greater than the ...
... Hypothesis . the angle ACD is equal to the angle ADC . [ I. 5 . But the angle ACD is greater than the angle BCD , [ Ax . 9 . therefore the angle ADC is also greater than the angle BCD ; much more then is the angle BDC greater than the ...
Seite 16
... B draw BE at right angles to AB . Then , because ABC is a straight line , the angle CBE is equal to the angle EBA . E B [ Hypothesis . [ Definition 10 . Also , because ABD is a straight line , the 16 EUCLID'S ELEMENTS .
... B draw BE at right angles to AB . Then , because ABC is a straight line , the angle CBE is equal to the angle EBA . E B [ Hypothesis . [ Definition 10 . Also , because ABD is a straight line , the 16 EUCLID'S ELEMENTS .
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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