The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth ... Also the Book of Euclid's Data, in Like Manner CorrectedWingrave and Collingwood, 1816 - 528 Seiten |
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Seite 13
... two triangles that have their sides which are terminated in one extremity of the base equal to one another , and ... given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given rectilineal angle , it is ...
... two triangles that have their sides which are terminated in one extremity of the base equal to one another , and ... given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given rectilineal angle , it is ...
Seite 54
... divide a given straight line into two parts , so that the rectangle contained by the whole , and one of the parts , shall be equal to the square of the other part . Let AB be the given straight line ; it is required to di- vide it into ...
... divide a given straight line into two parts , so that the rectangle contained by the whole , and one of the parts , shall be equal to the square of the other part . Let AB be the given straight line ; it is required to di- vide it into ...
Seite 178
... given straight line to apply a parallelogram equal to a given rectilineal ... Let AB be the given straight line , and C the given rec- tilineal figure ... Divide AB into two 10. 1. equal parts in the point C E , and upon EB de- D K N ...
... given straight line to apply a parallelogram equal to a given rectilineal ... Let AB be the given straight line , and C the given rec- tilineal figure ... Divide AB into two 10. 1. equal parts in the point C E , and upon EB de- D K N ...
Seite 179
... Let KL be the homologous side to EG , and LM to GF ; and because EF is equal to C and KM together , EF is greater than KM ; therefore the straight line EG is greater than KL , and GF than LM : Make GX equal to LK , and GO equal to LM ...
... Let KL be the homologous side to EG , and LM to GF ; and because EF is equal to C and KM together , EF is greater than KM ; therefore the straight line EG is greater than KL , and GF than LM : Make GX equal to LK , and GO equal to LM ...
Häufige Begriffe und Wortgruppen
ABC is given ABCD AC is equal altitude angle ABC angle BAC base BC bisected Book XI centre circle ABC circumference common logarithm cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given point given ratio given straight line gnomon greater join less Let ABC logarithm multiple opposite parallel parallelogram AC perpendicular point F polygon prism proportionals proposition 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 parallelopipeds square of BC straight line AB straight line BC tangent THEOR third triangle ABC vertex wherefore
Beliebte Passagen
Seite 41 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Seite 180 - 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.
Seite 166 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. Let AC, CF be equiangular parallelograms having the angle BCD equal to the angle ECG ; the ratio of the parallelogram AC to the parallelogram CF is the same with the ratio which is compounded •f the ratios of their sides. DH Let BC, CG be placed in a straight line ; therefore DC and CE are also in a straight line (14.
Seite 2 - A rhomboid, is that which has its opposite sides equal to one another, but all its sides are not equal, nor its angles right angles.
Seite 105 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...
Seite 79 - 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.
Seite 1 - A straight line is that which lies evenly between its extreme points.
Seite 149 - 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.
Seite 23 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Seite 83 - Wherefore from the given circle ABC has been cut off the segment BAC, containing an angle equal to the given angle DQEP PROP. XXXV. THEOR. If two straight lines within a circle cut one another, the rectangle contained by the segments of one of them is equal to the rectangle contained by the segments of the other. Let the...