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 TrigonometryPrinted and published at no. 24 Arch Street, A. Walker, Agent, 1832 - 333 σελίδες |
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Σελίδα 22
... equal ( 11. Definition ) to AB ; and because the point B is the centre of the circle ACE , BC is equal to AB : But ... ABC is therefore equilateral , and it is described upon the given straight line AB . Which was required to be done . PROP .
... equal ( 11. Definition ) to AB ; and because the point B is the centre of the circle ACE , BC is equal to AB : But ... ABC is therefore equilateral , and it is described upon the given straight line AB . Which was required to be done . PROP .
Σελίδα 23
... equal to the remainder ( 3. Ax . ) BG : But it has been shewn that BC is equal to BG ; wherefore AL and BC are each ... ABC , DEF be two triangles which have the two sides AB , AC equal to the two sides DE , DF , each to each , viz.AB to ...
... equal to the remainder ( 3. Ax . ) BG : But it has been shewn that BC is equal to BG ; wherefore AL and BC are each ... ABC , DEF be two triangles which have the two sides AB , AC equal to the two sides DE , DF , each to each , viz.AB to ...
Σελίδα 24
... ABC to the angle DEF , and the angle ACB to DFE . For , if the triangle ABC be applied to the triangle DEF , so that ... equal to DE ; and AB coinciding with DE , AC shall coincide with DF , because the angle BAC is equal to the angle ...
... ABC to the angle DEF , and the angle ACB to DFE . For , if the triangle ABC be applied to the triangle DEF , so that ... equal to DE ; and AB coinciding with DE , AC shall coincide with DF , because the angle BAC is equal to the angle ...
Σελίδα 25
... equal to the angle GCB , and the angle BCF to the angle CBG . Now , since it has been demon- strated , that the whole angle ABG is equal to the whole ACF , and the part CBG , to the part BCF the remaining angle ABC is therefore equal to ...
... equal to the angle GCB , and the angle BCF to the angle CBG . Now , since it has been demon- strated , that the whole angle ABG is equal to the whole ACF , and the part CBG , to the part BCF the remaining angle ABC is therefore equal to ...
Σελίδα 26
... equal to DB ; then , in the case in which the vertex of each of the triangles is without the other tri- angle ... ABC , DEF be two triangles having the two sides AB , AC , equal to the two sides DE , DF , each to each , viz . AB to DE ...
... equal to DB ; then , in the case in which the vertex of each of the triangles is without the other tri- angle ... ABC , DEF be two triangles having the two sides AB , AC , equal to the two sides DE , DF , each to each , viz . AB to DE ...
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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 parallelopipeds perpendicular polygon prism PROB proportional 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 parallelopipeds spherical angle spherical triangle SPHERICAL TRIGONOMETRY square straight line AC THEOR third touches the circle triangle ABC 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 41 - 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 together equal to two right angles.
Σελίδα 36 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 33 - ANY two sides of a triangle are together greater than the third side.
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 308 - 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.
Σελίδα 25 - UPON the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity...
Σελίδα 56 - If a straight line be bisected, and produced to any point, the rectangle contained by the whole line thus produced, and the part of it produced, together with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.
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 90 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.