The Elements of EuclidDesilver, Thomas, 1838 - 416 sider |
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Side 11
... drawn equal to the given straight line BC . Which was to be done . PROP . III . PROB . FROM the greater of two given ... draw ( 2. 1. ) the straight line AD equal to C ; and from the centre A , and at the dis- tance AD , describe ( 3 ...
... drawn equal to the given straight line BC . Which was to be done . PROP . III . PROB . FROM the greater of two given ... draw ( 2. 1. ) the straight line AD equal to C ; and from the centre A , and at the dis- tance AD , describe ( 3 ...
Side 16
... draw a straight line from the point C at right angles to AB . * Take any point D in AC , and ( 3. 1. ) make CE equal to CD , and upon DE describe ( 1. 1. ) the equilateral triangle , DFE , and join FC ; the straight line FC drawn from ...
... draw a straight line from the point C at right angles to AB . * Take any point D in AC , and ( 3. 1. ) make CE equal to CD , and upon DE describe ( 1. 1. ) the equilateral triangle , DFE , and join FC ; the straight line FC drawn from ...
Side 17
... drawn from the given point C , is per- pendicular to the given straight line AB . A F C H G B Ꭰ Because FH is equal to HG , and HC , common to the two trian- gles FHC , GHC , the two sides FH , HC are equal to the two GH , HC , each to ...
... drawn from the given point C , is per- pendicular to the given straight line AB . A F C H G B Ꭰ Because FH is equal to HG , and HC , common to the two trian- gles FHC , GHC , the two sides FH , HC are equal to the two GH , HC , each to ...
Side 21
... drawn two straight lines to a point within the triangle , these shall be less than the other two sides of the triangle , but shall contain a greater angle . * Let the two straight lines BD , CD be drawn from B , C , the ends of the side ...
... drawn two straight lines to a point within the triangle , these shall be less than the other two sides of the triangle , but shall contain a greater angle . * Let the two straight lines BD , CD be drawn from B , C , the ends of the side ...
Side 28
... draw a straight line through a given point parallel to a given straight line . A F Let A be the given point , and BC ... drawn through the given point A parallel to the given straight line BC . Which was to be done . PROP . XXXII . THEOR ...
... draw a straight line through a given point parallel to a given straight line . A F Let A be the given point , and BC ... drawn through the given point A parallel to the given straight line BC . Which was to be done . PROP . XXXII . THEOR ...
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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.