The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh and Twelfth ; the Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored ; Also the Book of Euclid's Data, in Like Manner CorrectedDesilver, 1829 - 516 sider |
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Side 13
... given finite straight line . Let AB be the given straight line ; it is ... BC is equal to BA : but it has been proved that CA is equal to AB ... BC are equal to one another : and the triangle ABC is therefore equilateral , and it is ...
... given finite straight line . Let AB be the given straight line ; it is ... BC is equal to BA : but it has been proved that CA is equal to AB ... BC are equal to one another : and the triangle ABC is therefore equilateral , and it is ...
Side 14
... BC is equal to G , wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC . Wherefore from the given point A a straight line AL ...
... BC is equal to G , wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC . Wherefore from the given point A a straight line AL ...
Side 19
... BC is equal to EF ; therefore BC coin- ciding with EF , BA and AC shall coincide with ED and DF ; for , if the base ... given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given rectilineal angle , it ...
... BC is equal to EF ; therefore BC coin- ciding with EF , BA and AC shall coincide with ED and DF ; for , if the base ... given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given rectilineal angle , it ...
Side 34
... given straight line . E A F Let A be the given point , and BC the given straight line ; it is required to draw a straight line through the point A , parallel to the straight line BC . In BC take any point D , and join AD ; and at the ...
... given straight line . E A F Let A be the given point , and BC the given straight line ; it is required to draw a straight line through the point A , parallel to the straight line BC . In BC take any point D , and join AD ; and at the ...
Side 35
... BC , EF , makes the alternate angles EAD , ADC equal to one another , EF is parallel ( 27. 1. ) to BC . Therefore the straight line EAF is drawn through the given point A parallel to the given straight line BC . Which was to be done ...
... BC , EF , makes the alternate angles EAD , ADC equal to one another , EF is parallel ( 27. 1. ) to BC . Therefore the straight line EAF is drawn through the given point A parallel to the given straight line BC . Which was to be done ...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2018 |
Vanlige uttrykk og setninger
altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference co-sine 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 gnomon greater join less Let ABC multiple parallel parallelogram 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 AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
Populære avsnitt
Side 9 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 81 - The angles in the same segment of a circle are equal to one another.
Side 315 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Side 33 - 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 49 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Side 96 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Side 155 - 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 22 - ANY two angles of a triangle are together less than two right angles.
Side 25 - Let A, B, C be the three given straight lines, of which any two whatever are greater than the third, viz.
Side 24 - Any two sides of a triangle are together greater than the third side.