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, 1853 - 317 páginas |
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Página 13
... equal to one another ; therefore the straight line AL is equal to BC . Wherefore , from the given point A , a ... angles contained by those sides equal to one another , their bases , or third sides , shall be equal ; and the areas of the ...
... equal to one another ; therefore the straight line AL is equal to BC . Wherefore , from the given point A , a ... angles contained by those sides equal to one another , their bases , or third sides , shall be equal ; and the areas of the ...
Página 14
... equal to the angle EDF ; wherefore also the point C shall coincide with the point F , because AC is equal to DF ... angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the angle ABC to ...
... equal to the angle EDF ; wherefore also the point C shall coincide with the point F , because AC is equal to DF ... angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the angle ABC to ...
Página 15
... equal to the angle GCB , which are the angles upon the oth of the base . COROLLARY . Hence every equilateral triangle is also equiangular PROP . VI . THEOR . If two angles of a triangle be equal to one another , the sides which subtend ...
... equal to the angle GCB , which are the angles upon the oth of the base . COROLLARY . Hence every equilateral triangle is also equiangular PROP . VI . THEOR . If two angles of a triangle be equal to one another , the sides which subtend ...
Página 16
... equal to AD in the triangle CD , the 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 the angle BCD ; wherefore the angle FDC is likewise greater than BCD ; E F B ...
... equal to AD in the triangle CD , the 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 the angle BCD ; wherefore the angle FDC is likewise greater than BCD ; E F B ...
Página 17
... 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 angle , it is required ...
... 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 angle , it is required ...
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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 51 - 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 74 - THE angles in the same segment of a circle are equal to one another...
Página 37 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Página 29 - 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 29 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line through EAF the point A, parallel to the straight line '
Página 147 - If the vertical angle of a triangle be bisected by a straight line which also cute the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Página 19 - The angles which one straight line makes with another upon one side of i't, are either two right angles, or are together eqval to two right angles.
Página 134 - IF three straight lines be proportionals, the rectangle contained by the extremes is equal to the square of the mean : and if the rectangle contained by the extremes be equal to the square of the mean, the three straight lines are proportionals.
Página 294 - 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 13 - BC. Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC.