The Elements of Euclid for the Use of Schools and CollegesMacmillan, 1872 - 400 sider |
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Side xv
... construction then usually follows , which states the necessary straight lines and circles which must be drawn in ... construction is required ; and sometimes the construction and demonstration are com- bined . The demonstration is a ...
... construction then usually follows , which states the necessary straight lines and circles which must be drawn in ... construction is required ; and sometimes the construction and demonstration are com- bined . The demonstration is a ...
Side xvi
... construction that has been made , or which are given in the supposition of the proposition itself . The word hypothesis is used in the same sense as supposition . To assist the student in following the steps of the reasoning ...
... construction that has been made , or which are given in the supposition of the proposition itself . The word hypothesis is used in the same sense as supposition . To assist the student in following the steps of the reasoning ...
Side 16
... Construction . and CF is common to the two triangles DCF , ECF ; the two sides DC , CF are equal to the two sides EC , CF , each to each ; and the base DF is equal to the base EF ; [ Definition 24 . therefore the angle DCF is equal to ...
... Construction . and CF is common to the two triangles DCF , ECF ; the two sides DC , CF are equal to the two sides EC , CF , each to each ; and the base DF is equal to the base EF ; [ Definition 24 . therefore the angle DCF is equal to ...
Side 17
... Construction . and HC is common to the two triangles FHC , GHC ; the two sides FH , HC are equal to the two sides GH , HC , each to each ; [ Definition 15 . and the base CF is equal to the base CG ; therefore the angle CHF is equal to ...
... Construction . and HC is common to the two triangles FHC , GHC ; the two sides FH , HC are equal to the two sides GH , HC , each to each ; [ Definition 15 . and the base CF is equal to the base CG ; therefore the angle CHF is equal to ...
Side 23
... Construction . [ I. 5 . Then , because AD is equal to AC , the angle ADC is equal to the angle ACD . But the angle BCD is greater than the angle ACD . [ Ax . 9 . Therefore the angle BCD is greater than the angle BDC . And because the ...
... Construction . [ I. 5 . Then , because AD is equal to AC , the angle ADC is equal to the angle ACD . But the angle BCD is greater than the angle ACD . [ Ax . 9 . Therefore the angle BCD is greater than the angle BDC . And because the ...
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Vanlige uttrykk og setninger
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