The Elements of Euclid for the Use of Schools and Colleges: Comprising the First Six Books and Portions of the Eleventh and Twelfth Books : with Notes, an Appendix, and ExercisesMacmillan, 1867 - 400 páginas |
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Página 3
... centre of the circle . 17. A diameter of a circle is a straight line drawn through the centre , and terminated both ways by the cir- cumference . [ A radius of a circle is a straight line drawn from the centre to the circumference ...
... centre of the circle . 17. A diameter of a circle is a straight line drawn through the centre , and terminated both ways by the cir- cumference . [ A radius of a circle is a straight line drawn from the centre to the circumference ...
Página 5
... centre , at any distance from that centre . AXIOMS . 1. Things which are equal to the same DEFINITIONS . 5.
... centre , at any distance from that centre . AXIOMS . 1. Things which are equal to the same DEFINITIONS . 5.
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... centre A , at the distance AB , describe the circle BCD . [ Postulate 3 . From the centre B , at the distance BA , describe the circle ACE . [ Postulate 3 . From the point C , at which the circles cut one another , draw the straight ...
... centre A , at the distance AB , describe the circle BCD . [ Postulate 3 . From the centre B , at the distance BA , describe the circle ACE . [ Postulate 3 . From the point C , at which the circles cut one another , draw the straight ...
Página 8
... centre B , at the dis- tance BC , describe the circle CGH , meeting DF at G. [ Post . 3 . From the centre D , at the dis- tance DG , describe the circle GKL , meeting DE at L. [ Post . 3 . AL shall be equal to BC . B 42 Because the ...
... centre B , at the dis- tance BC , describe the circle CGH , meeting DF at G. [ Post . 3 . From the centre D , at the dis- tance DG , describe the circle GKL , meeting DE at L. [ Post . 3 . AL shall be equal to BC . B 42 Because the ...
Página 9
... centre A , at the distance AD , describe the circle DEF meeting AB at E. [ Postulate 3 . AE shall be equal to C. Because the point A is the centre of the circle DEF , AE is equal to AD . But C is equal to AD . [ Definition 15 ...
... centre A , at the distance AD , describe the circle DEF meeting AB at E. [ Postulate 3 . AE shall be equal to C. Because the point A is the centre of the circle DEF , AE is equal to AD . But C is equal to AD . [ Definition 15 ...
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Términos y frases comunes
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 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
Pasajes populares
Página 35 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.
Página 67 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side 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...
Página 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.
Página 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.
Página 50 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Página 57 - If a straight line be divided into two equal parts, and also into two unequal parts ; the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Página 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.
Página 227 - If two straight lines be at right angles to the same plane, they shall be parallel to one another. Let the straight lines AB, CD be at right angles to the same plane : AB is parallel to CD.
Página 102 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Página 352 - Prove that the square on any straight line drawn from the vertex of an isosceles triangle to the base, is less than the square on a side of the triangle by the rectangle contained by the segments of the base : and conversely.