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 |
Dentro del libro
Resultados 1-5 de 100
Página xv
... angle , nor that the equal sides are opposite to equal angles , nor lastly , that things equal to the same thing are equal to one another ? By a scientific mind this information will not be thought lightly of ; and it is exactly that ...
... angle , nor that the equal sides are opposite to equal angles , nor lastly , that things equal to the same thing are equal to one another ? By a scientific mind this information will not be thought lightly of ; and it is exactly that ...
Página 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 ... angles contain- ed by those sides equal to one another , their bases , or third sides , shall be equal ; and the ...
... equal to the remainder ( 3. Ax . ) BG : But it has been shewn that BC is equal to BG ; wherefore AL and BC are each ... angles contain- ed by those sides equal to one another , their bases , or third sides , shall be equal ; and the ...
Página 24
... equal to DE ; and AB coinciding with DE , AC shall coincide with DF , because the angle BAC is equal to the angle ... angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the an- gle ABC ...
... equal to DE ; and AB coinciding with DE , AC shall coincide with DF , because the angle BAC is equal to the angle ... angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the an- gle ABC ...
Página 25
... equal to the two CG , GB , each to each ; but the angle BFC is equal to the angle CGB ; wherefore the triangles BFC , CGB are equal ( 3.1 . ) and their remaining angles are equal , to which the equal sides . are opposite ; therefore the ...
... equal to the two CG , GB , each to each ; but the angle BFC is equal to the angle CGB ; wherefore the triangles BFC , CGB are equal ( 3.1 . ) and their remaining angles are equal , to which the equal sides . are opposite ; therefore the ...
Página 26
... equal to DB ; then , in the case in which the vertex of each of the triangles is without the other tri- angle ... angles ECD , FDC upon the other side of the base CD are equal ( 5. 1. ) to one another , but the angle ECD is greater than ...
... equal to DB ; then , in the case in which the vertex of each of the triangles is without the other tri- angle ... angles ECD , FDC upon the other side of the base CD are equal ( 5. 1. ) to one another , but the angle ECD is greater than ...
Otras ediciones - Ver todas
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.