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 TrigonometryW. E. Dean, 1847 - 317 páginas |
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Página 12
... wherefore CA , AB , CB are equal to one another ; and the triangle ABC is therefore equilateral , and it is described upon the given straight line AB . PROP . II . PROB . From a given point to draw a straight line equal to a given ...
... wherefore CA , AB , CB are equal to one another ; and the triangle ABC is therefore equilateral , and it is described upon the given straight line AB . PROP . II . PROB . From a given point to draw a straight line equal to a given ...
Página 13
... Wherefore , from the given point A , a straight line AL has been drawn equal to the given straight line BC . PROP . III . PROB . From the greater of two given straight lines to cut off a part equal to the less . Let AB and C be the two ...
... Wherefore , from the given point A , a straight line AL has been drawn equal to the given straight line BC . PROP . III . PROB . From the greater of two given straight lines to cut off a part equal to the less . Let AB and C be the two ...
Página 14
... 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 . def . 3. ) , and shall be equal to it ...
... 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 . def . 3. ) , and shall be equal to it ...
Página 16
... wherefore the angle FDC is likewise greater than BCD ; much more then is the angle BDC greater than the angle BCD . Again , because CB is equal to DB , the angle BDC is equal ( 5. 1. ) to the angle BCD ; but BDC has been proved to be ...
... wherefore the angle FDC is likewise greater than BCD ; much more then is the angle BDC greater than the angle BCD . Again , because CB is equal to DB , the angle BDC is equal ( 5. 1. ) to the angle BCD ; but BDC has been proved to be ...
Página 17
... wherefore likewise the angle BAC coincides with the angle EDF , and is equal ( 8. Ax . ) to it . PROP . IX . PROB . To bisect a given rectilineal angle , that is , to divide it into two equal angles . A Let BAC be the given rectilineal ...
... wherefore likewise the angle BAC coincides with the angle EDF , and is equal ( 8. Ax . ) to it . PROP . IX . PROB . To bisect a given rectilineal angle , that is , to divide it into two equal angles . A Let BAC be the given rectilineal ...
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Términos y frases comunes
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated described diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROB PROP proportional proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR touches the circle triangle ABC triangle DEF wherefore
Pasajes populares
Página 53 - 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 18 - If two triangles have two sides of the one equal to two sides of the...
Página 54 - 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 82 - 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 31 - Straight lines which are parallel to the same straight line are parallel to one another. Triangles and Rectilinear Figures. The sum of the angles of a triangle is equal to two right angles.
Página 11 - 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 21 - The angles which one straight line makes with another upon one side of it, are either two right angles, or are together equal to two right angles. Let the straight line AB make with CD, upon one side of it, the angles CBA, ABD : these shall either be two right angles, or shall together be equal to two right angles. For...
Página 101 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Página 58 - AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part.
Página 298 - 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.