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 21
... produced to any length both ways , and let C be a point without it . It is re- quired to draw a straight line per- pendicular to AB from the point C. Take any point D upon the other side of AB , and from the centre C , at the distance ...
... produced to any length both ways , and let C be a point without it . It is re- quired to draw a straight line per- pendicular to AB from the point C. Take any point D upon the other side of AB , and from the centre C , at the distance ...
Side 24
... produced , the exterior an- gle is greater than either of the interior opposite angles . Let ABC be a triangle , and let its side BC be produced to D , the exterior angle ACD is greater than either of the interior op- ⚫posite angles ...
... produced , the exterior an- gle is greater than either of the interior opposite angles . Let ABC be a triangle , and let its side BC be produced to D , the exterior angle ACD is greater than either of the interior op- ⚫posite angles ...
Side 26
... Produce BA to the point D , and make ( 3. 1. ) AD equal to AC ; and join DC . Because DA is equal to AC , the angle ADC is likewise equal ( 5. 1. ) to ACD ; but the angle BCD is great- er than the angle ACD ; therefore the angle BCD is ...
... Produce BA to the point D , and make ( 3. 1. ) AD equal to AC ; and join DC . Because DA is equal to AC , the angle ADC is likewise equal ( 5. 1. ) to ACD ; but the angle BCD is great- er than the angle ACD ; therefore the angle BCD is ...
Side 32
... produced shall meet either towards B , D , or towards A , C ; let them be produced and meet towards B , D , in the point G ; therefore GEF is a tri- angle , and its exterior angle AEF is greater ( 16. 1. ) than the in- terior and ...
... produced shall meet either towards B , D , or towards A , C ; let them be produced and meet towards B , D , in the point G ; therefore GEF is a tri- angle , and its exterior angle AEF is greater ( 16. 1. ) than the in- terior and ...
Side 33
... AB , CD , if produced far enough , shall meet ; but they never meet , since they are parallel * See the Notes to this Proposition . E by the hypothesis ; therefore the angle AGH is not BOOK I. 33 THE ELEMENTS OF EUCLID .
... AB , CD , if produced far enough , shall meet ; but they never meet , since they are parallel * See the Notes to this Proposition . E by the hypothesis ; therefore the angle AGH is not BOOK I. 33 THE ELEMENTS OF EUCLID .
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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.