The Elements of Euclid for the Use of Schools and CollegesMacmillan, 1872 - 400 Seiten |
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Seite 6
... double of the same thing are equal to one another . 7. Things which are halves of the same thing are equal to one another . 8. Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one ...
... double of the same thing are equal to one another . 7. Things which are halves of the same thing are equal to one another . 8. Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one ...
Seite 39
... double of the triangle BDC ; B and they are therefore equal to one another . But if the sides AD , EF , opposite to the of the parallelo- DE F [ I. 34 . [ Axiom 6 . base BC D grams ABCD , EBCF be not terminated at the same point , then ...
... double of the triangle BDC ; B and they are therefore equal to one another . But if the sides AD , EF , opposite to the of the parallelo- DE F [ I. 34 . [ Axiom 6 . base BC D grams ABCD , EBCF be not terminated at the same point , then ...
Seite 43
... double of the triangle . Let the parallelogram ABCD and the triangle EBC be on the same base BC , and between the same parallels BC , AE : the parallelogram ABCD shall be double of the triangle EBC . Join AC . Then the triangle ABC is ...
... double of the triangle . Let the parallelogram ABCD and the triangle EBC be on the same base BC , and between the same parallels BC , AE : the parallelogram ABCD shall be double of the triangle EBC . Join AC . Then the triangle ABC is ...
Seite 44
... double of the triangle AEC . But the parallelogram FECG is also double of the triangle AEC , because they are on the same base EC , and between the same parallels EC , AG . [ I. 41 . Therefore the parallelogram FECG is equal to the ...
... double of the triangle AEC . But the parallelogram FECG is also double of the triangle AEC , because they are on the same base EC , and between the same parallels EC , AG . [ I. 41 . Therefore the parallelogram FECG is equal to the ...
Seite 50
... to each ; [ Definition 30 . and the angle DBA is equal to the angle FBC ; therefore the triangle ABD is equal to the triangle FBC . [ I. 4 . Now the parallelogram BL is double of the triangle ABD 50 EUCLID'S ELEMENTS .
... to each ; [ Definition 30 . and the angle DBA is equal to the angle FBC ; therefore the triangle ABD is equal to the triangle FBC . [ I. 4 . Now the parallelogram BL is double of the triangle ABD 50 EUCLID'S ELEMENTS .
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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