The Elements of EuclidDesilver, Thomas, 1838 - 416 sider |
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Side 53
... circle , are those in which the angles are equal , or which contain equal angles . PROP . I. PROB . To find the centre of a given circle . * Let ABC be the given circle ; it is required to find its centre . Draw within it any straight line ...
... circle , are those in which the angles are equal , or which contain equal angles . PROP . I. PROB . To find the centre of a given circle . * Let ABC be the given circle ; it is required to find its centre . Draw within it any straight line ...
Side 54
... circle ABC . Which was to be found . с G F A B D E COR . From this it is manifest , that if in a circle a straight line bisect another at right angles , the centre of the circle is in the line which bisects the other . PROP . II . THEOR ...
... circle ABC . Which was to be found . с G F A B D E COR . From this it is manifest , that if in a circle a straight line bisect another at right angles , the centre of the circle is in the line which bisects the other . PROP . II . THEOR ...
Side 55
... circle , and join EA , EB . Then , because AF is equal to FB , and FE common to the two triangles AFE , BFE , there ... ABCD be a circle , and AC , BD two straight lines in it which cut one another in the point E , and do not both pass ...
... circle , and join EA , EB . Then , because AF is equal to FB , and FE common to the two triangles AFE , BFE , there ... ABCD be a circle , and AC , BD two straight lines in it which cut one another in the point E , and do not both pass ...
Side 56
... a circle , & c . Q. E. D. PROP . V. THEOR . Ir two circles cut one another , they shall not have the same centre . Let the two circles ABC , CDG cut one another in the points B , C ; they have not the same centre . C For , if it be ...
... a circle , & c . Q. E. D. PROP . V. THEOR . Ir two circles cut one another , they shall not have the same centre . Let the two circles ABC , CDG cut one another in the points B , C ; they have not the same centre . C For , if it be ...
Side 57
... ABCD be a circle , and AD its diameter , in which let any point E be taken which is not the centre ; let the centre be E ; of all the straight lines FB , FC , FG , & c . that can be drawn from F to the circumference , FA is the greatest ...
... ABCD be a circle , and AD its diameter , in which let any point E be taken which is not the centre ; let the centre be E ; of all the straight lines FB , FC , FG , & c . that can be drawn from F to the circumference , FA is the greatest ...
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altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gles gnomon greater join less Let ABC multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopiped square of AC square of BC straight line AB straight line BC tangent THEOR triangle ABC triplicate ratio vertex wherefore
Populære avsnitt
Side 34 - If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.
Side 143 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts 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.
Side 63 - 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.
Side 246 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
Side 9 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Side 119 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 19 - 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.
Side 12 - To construct a triangle of which the sides shall be equal to three given straight lines ; but any two whatever of these lines must be greater than the third (20.
Side 78 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Side 131 - ... rectilineal figures are to one another in the duplicate ratio of their homologous sides.