The Elements of Euclid for the Use of Schools and Colleges: With Notes, an Appendix, and Exercises. comprising the first six books and portions of the eleventh and twelfth booksMacmillan and Company, 1880 - 400 sider |
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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 ...
Side 138
... fourth , and the fifth the same multiple of the second that the sixth is of the fourth ; the first toge- ther with the fifth shall be the same multiple of the second , that the third together with the sixth is of the fourth . Let AB the ...
... fourth , and the fifth the same multiple of the second that the sixth is of the fourth ; the first toge- ther with the fifth shall be the same multiple of the second , that the third together with the sixth is of the fourth . Let AB the ...
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ... Issac Todhunter Ingen forhåndsvisning tilgjengelig - 2014 |
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
Populære avsnitt
Side 225 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Side 284 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 73 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a Right Angle; and the straight line which stands on the other is called a Perpendicular to it.
Side 39 - Triangles upon the same base, and between the same parallels, are equal to one another.
Side 10 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Side 353 - AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part.
Side 67 - ... subtending the obtuse angle, is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse angle, Let ABC be an obtuse-angled triangle, having the obtuse angle ACB; and from the point A, let AD be drawn perpendicular to BC produced.
Side 300 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.
Side xv - PROPOSITION I. PROBLEM. To describe an equilateral triangle upon a given Jinite straight line. Let AB be the given straight line. It is required to describe an equilateral triangle upon AB, From the centre A, at the distance AB, describe the circle BCD ; (post.
Side 36 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.