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 11
... which are the angles on the other side of the base . Wherefore , the angles & c . Q.E.D. Corollary . Hence every equilateral triangle is also equiangular . PROPOSITION 6. THEOREM . If two angles of a triangle BOOK I. 5 . 11.
... which are the angles on the other side of the base . Wherefore , the angles & c . Q.E.D. Corollary . Hence every equilateral triangle is also equiangular . PROPOSITION 6. THEOREM . If two angles of a triangle BOOK I. 5 . 11.
Side 12
... Corollary . equilateral . Hence every equiangular triangle is also PROPOSITION 7. THEOREM . On the same base , and on the same side of it , there can- not be two triangles having their sides which are terminated at one extremity of the ...
... Corollary . equilateral . Hence every equiangular triangle is also PROPOSITION 7. THEOREM . On the same base , and on the same side of it , there can- not be two triangles having their sides which are terminated at one extremity of the ...
Side 16
... Corollary . By the help of this problem it may be shewn that two straight lines cannot have a common segment . If it be possible , let the two straight lines ABC , ABD have the segment AB com- mon to both of them . From the point B draw ...
... Corollary . By the help of this problem it may be shewn that two straight lines cannot have a common segment . If it be possible , let the two straight lines ABC , ABD have the segment AB com- mon to both of them . From the point B draw ...
Side 20
... Corollary 1. From this it is manifest that , if two straight lines cut one another , the angles which they make at the point where they cut , are together equal to four right angles . Corollary 2. And consequently , that all the angles ...
... Corollary 1. From this it is manifest that , if two straight lines cut one another , the angles which they make at the point where they cut , are together equal to four right angles . Corollary 2. And consequently , that all the angles ...
Side 35
... angles GBA , BAO , ACB are together equal to two right angles . at [ I. 13 . [ Axiom 1 . Wherefore , if a side of any triangle & c . Q.E.D. COROLLARY 1. All the interior angles of any recti- lineal 3-2 BOOK I. 31 , 32 . 35.
... angles GBA , BAO , ACB are together equal to two right angles . at [ I. 13 . [ Axiom 1 . Wherefore , if a side of any triangle & c . Q.E.D. COROLLARY 1. All the interior angles of any recti- lineal 3-2 BOOK I. 31 , 32 . 35.
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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.