The Elements of Euclid for the Use of Schools and CollegesMacmillan, 1872 - 400 sider |
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... Fourth Edition . Crown 8vo . cloth . 58 . 3. A Treatise on Spherical Trigono- 9 . metry for the use of Colleges and Schools . Second Edition . Crown 8vo . cloth . 48. 6d . A Treatise on Conic Sections . With numerous Examples . Fourth ...
... Fourth Edition . Crown 8vo . cloth . 58 . 3. A Treatise on Spherical Trigono- 9 . metry for the use of Colleges and Schools . Second Edition . Crown 8vo . cloth . 48. 6d . A Treatise on Conic Sections . With numerous Examples . Fourth ...
Side 134
... fourth , when any equimultiples whatever of the first and the third being taken , and any equimultiples whatever of the second and the fourth , if the multiple of the first be less than that of the second , the multiple of the third is ...
... fourth , when any equimultiples whatever of the first and the third being taken , and any equimultiples whatever of the second and the fourth , if the multiple of the first be less than that of the second , the multiple of the third is ...
Side 135
... fourth ; and the third is said to have to the fourth a less ratio than the first has to the second . 8. Analogy , or proportion , is the similitude of ratios . 9. Proportion consists in three terms at least . 10. When three magnitudes ...
... fourth ; and the third is said to have to the fourth a less ratio than the first has to the second . 8. Analogy , or proportion , is the similitude of ratios . 9. Proportion consists in three terms at least . 10. When three magnitudes ...
Side 136
... fourth . V. 16 . 14. Invertendo , by inversion ; when there are four proportionals , and it is inferred , that the second is to the first as the fourth is to the third . V. B. 15. Componendo , by composition ; when there are four ...
... fourth . V. 16 . 14. Invertendo , by inversion ; when there are four proportionals , and it is inferred , that the second is to the first as the fourth is to the third . V. B. 15. Componendo , by composition ; when there are four ...
Side 137
... fourth of the first rank , as the last but three is to the last but two of the second rank ; and so on in a cross order ; and the inference is that mentioned in the eighteenth definition . V. 23 . AXIOMS . 1. Equimultiples of the same ...
... fourth of the first rank , as the last but three is to the last but two of the second rank ; and so on in a cross order ; and the inference is that mentioned in the eighteenth definition . V. 23 . AXIOMS . 1. Equimultiples of the same ...
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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