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 páginas |
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Página ix
... demonstrating more casily some of the properties of parallel lines . In the third Book , the remarks con- cerning the angles made by a straight line , and the circumference of a circle , are left out , as tending to perplex one who has ...
... demonstrating more casily some of the properties of parallel lines . In the third Book , the remarks con- cerning the angles made by a straight line , and the circumference of a circle , are left out , as tending to perplex one who has ...
Página xv
... demonstrate that any two sides of a triangle are greater than the third ; it may be replied , that this is no doubt a truth which , with- out proof , most men will be inclined to admit ; but are we for that reason to account it of no ...
... demonstrate that any two sides of a triangle are greater than the third ; it may be replied , that this is no doubt a truth which , with- out proof , most men will be inclined to admit ; but are we for that reason to account it of no ...
Página 24
... demonstrated . PROP . V. THEOR . 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 also be equal . Let ABC be an isosceles ...
... demonstrated . PROP . V. THEOR . 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 also be equal . Let ABC be an isosceles ...
Página 26
... demonstrated to be greater than it ; which is impossible . D E But if one of the vertices , as D , be within the other triangle ACB ; produce AC , AD , to E , F ; therefore , because AC is equal to AD in the triangle ACD , the angles ...
... demonstrated to be greater than it ; which is impossible . D E But if one of the vertices , as D , be within the other triangle ACB ; produce AC , AD , to E , F ; therefore , because AC is equal to AD in the triangle ACD , the angles ...
Página 30
... demonstrated to be equal to the same three angles ; and things that are equal to the same are equal ( 1. Ax . ) to one another ; therefore the angles CBE , EBD are equal to the angles DBA , ABC ; but CBE , EBD , are two right angles ...
... demonstrated to be equal to the same three angles ; and things that are equal to the same are equal ( 1. Ax . ) to one another ; therefore the angles CBE , EBD are equal to the angles DBA , ABC ; but CBE , EBD , are two right angles ...
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Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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.
Página 36 - If two triangles have two sides of the one equal to two sides of the...
Página 33 - ANY two sides of a triangle are together greater than the third side.
Página 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.
Página 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.
Página 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...
Página 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.
Página 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.
Página 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.