Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids; to which are Added Elements of Plane and Spherical TrigonometryG. Long, 1819 - 333 σελίδες |
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Αποτελέσματα 1 - 5 από τα 56.
Σελίδα 23
... angle BAC be also equal to the angle EDF then shall the base BC be equal to the base EF ; and the triangle ABC to the tri- angle DEF ; and the other angles , to which the equal sides are op- A D ÄÄ B C E * The three conclusions in this ...
... angle BAC be also equal to the angle EDF then shall the base BC be equal to the base EF ; and the triangle ABC to the tri- angle DEF ; and the other angles , to which the equal sides are op- A D ÄÄ B C E * The three conclusions in this ...
Σελίδα 24
... angle BAC is equal to the angle EDF ; wherefore also the point C shall coincide with the point F , because AC is equal to DF : But the point B coincides with the point E ; wherefore the base BC shall coincide with the base EF ( cor ...
... angle BAC is equal to the angle EDF ; wherefore also the point C shall coincide with the point F , because AC is equal to DF : But the point B coincides with the point E ; wherefore the base BC shall coincide with the base EF ( cor ...
Σελίδα 27
... angle BAC coincides with the angle EDF , and is equal ( 8. Ax . ) to it . Therefore if two triangles , & c . Q. E. D. PROP . IX . PROB . To bisect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the ...
... angle BAC coincides with the angle EDF , and is equal ( 8. Ax . ) to it . Therefore if two triangles , & c . Q. E. D. PROP . IX . PROB . To bisect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the ...
Σελίδα 31
... BAC . Bisect ( 10. 1. ) AC in E , join BE and produce it to F , and make EF equal to BE ; join al- so FC , and produce AC to G. Because AE is equal to EC , and BE to EF ; AE , EB are e- qual to CE , EF , each to each ; and the angle AEB ...
... BAC . Bisect ( 10. 1. ) AC in E , join BE and produce it to F , and make EF equal to BE ; join al- so FC , and produce AC to G. Because AE is equal to EC , and BE to EF ; AE , EB are e- qual to CE , EF , each to each ; and the angle AEB ...
Σελίδα 32
... angle BCG , that is ( 15. 1. ) , the angle ACD , is greater than the angle ABC . Therefore , if one side , & c ... BAC , ACB , as also , CAB , ABC , are less than two right angles . Therefore , any two angles , & c . Q. E. D. B ...
... angle BCG , that is ( 15. 1. ) , the angle ACD , is greater than the angle ABC . Therefore , if one side , & c ... BAC , ACB , as also , CAB , ABC , are less than two right angles . Therefore , any two angles , & c . Q. E. D. B ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet opposite angle parallel parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle square straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore
Δημοφιλή αποσπάσματα
Σελίδα 56 - 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 of the line between the points of section, is equal to the square of half the line.
Σελίδα 19 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Σελίδα 33 - THE greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it.
Σελίδα 62 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the...
Σελίδα 62 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of 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...
Σελίδα 130 - 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.
Σελίδα 76 - THE diameter is the greatest straight line in a circle; and, of all others, that which is nearer to the centre is always greater than one more remote ; and the greater is nearer to the centre than the less.* Let ABCD be a circle, of which...
Σελίδα 36 - IF two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other.
Σελίδα 18 - 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.
Σελίδα 55 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.