Euclid's Elements [book 1-6] with corrections, by J.R. Young1838 |
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Resultater 1-5 af 87
Side 12
... AC is equal to AB ; and because the point B is the cen- 12 De tre of the circle ACE , BC is equal to BA : But it has been proved that CA is equal to AB ; therefore CA , CB , are each of them equal to AB ; but things which are equal to ...
... AC is equal to AB ; and because the point B is the cen- 12 De tre of the circle ACE , BC is equal to BA : But it has been proved that CA is equal to AB ; therefore CA , CB , are each of them equal to AB ; but things which are equal to ...
Side 14
... equal , each to euch , viz . those to which the equal sides are opposite . A Let ABC , DEF be two triangles , which have the two sides AB , AC , equal to the two sides DE , DF , each to each , viz . AB to DE , and AC to ' DF ; and the angle ...
... equal , each to euch , viz . those to which the equal sides are opposite . A Let ABC , DEF be two triangles , which have the two sides AB , AC , equal to the two sides DE , DF , each to each , viz . AB to DE , and AC to ' DF ; and the angle ...
Side 15
... equal to two sides of the other , each to each , and have like- wise the angles contained by those sides equal to ... AC , and let the straight lines AB , AC be produced to D and E : the angle ABC shall be equal to the angle ACB ; and ...
... equal to two sides of the other , each to each , and have like- wise the angles contained by those sides equal to ... AC , and let the straight lines AB , AC be produced to D and E : the angle ABC shall be equal to the angle ACB ; and ...
Side 16
... equal to the whole ACF , the parts of which , the angles CBG , BCF are also equal ; therefore the remaining angle ... AC . For , if AB be not equal to AC , one of them is greater than the other : let AB be the greater ; and from it cut ...
... equal to the whole ACF , the parts of which , the angles CBG , BCF are also equal ; therefore the remaining angle ... AC . For , if AB be not equal to AC , one of them is greater than the other : let AB be the greater ; and from it cut ...
Side 17
... equal to one another , and likewise their sides , CB , DB , that are ter- minated in B , equal to one another . B Join C , D ; then , in the case in which the vertex of each of the triangles is with- out the other triangle , because AC ...
... equal to one another , and likewise their sides , CB , DB , that are ter- minated in B , equal to one another . B Join C , D ; then , in the case in which the vertex of each of the triangles is with- out the other triangle , because AC ...
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Almindelige termer og sætninger
ABCD adjacent angles alternate angles angle ABC angle ACB angle BAC angle BCD angle EDF angles equal antecedent arc BC base BC BC is equal bisected centre circle ABC circumference consequent Const demonstrated described diameter double draw equal angles equal to AC equiangular equilateral and equiangular equimultiples Euclid exterior angle fore Geometry given circle given straight line gnomon greater inscribed join less Let ABC Let the straight logarithm multiple opposite angle parallel parallelogram pentagon perpendicular PROB proportion proposition Q. E. D. PROP radius rectangle contained rectilineal figure remaining angle segment side BC similar sine square of AC straight line AB straight line AC tangent THEOR touches the circle triangle ABC triangle DEF twice the rectangle wherefore
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Side 30 - IF two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other.
Side 105 - 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 50 - 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.
Side 61 - 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 on the line between the points of section, is equal to the square on half the line.
Side 65 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Side 70 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Side 41 - 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 172 - 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 45 - TRIANGLES upon the same base, and between the same parallels, are equal to one another.
Side 38 - If a, straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon the same side; and likewise the two interior angles upon the same side together equal to two right angles.