Elements of geometry: consisting of the first four,and the sixth, books of Euclid, with the principal theorems in proportion [&c.] by J. Narrien1842 |
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Resultat 1-5 av 78
Side
... produced by the revolution of a polygon in- scribed within , and of one described about the circle . Now Euclid , in proving ( Prop . 2. B. 12. ) by means of po- lygons inscribed in the circles , that circles are to one another as the ...
... produced by the revolution of a polygon in- scribed within , and of one described about the circle . Now Euclid , in proving ( Prop . 2. B. 12. ) by means of po- lygons inscribed in the circles , that circles are to one another as the ...
Side 5
... produced ever so far both ways , do not meet . ( A. ) A trapezium having two , only , of its sides parallel to one another is now called a trapezoid . POSTULATES . I. LET it be granted that a straight line may be drawn from any one ...
... produced ever so far both ways , do not meet . ( A. ) A trapezium having two , only , of its sides parallel to one another is now called a trapezoid . POSTULATES . I. LET it be granted that a straight line may be drawn from any one ...
Side 7
... produced . Now this is evidently a theorem which ought to have been previously demonstrated , whereas Euclid has made it one of his postulates ( Post . V. ) , and he thus leaves an elementary truth without direct support ; for there ...
... produced . Now this is evidently a theorem which ought to have been previously demonstrated , whereas Euclid has made it one of his postulates ( Post . V. ) , and he thus leaves an elementary truth without direct support ; for there ...
Side 8
... produce ( 2.Post . ) the straight lines DA , DB , to E and F : from the centre B , at the distance BC , describe ( 3. Post . ) the circle CGH , and from the centre D , at the distance DG , describe the circle G KL : AL shall be equal to ...
... produce ( 2.Post . ) the straight lines DA , DB , to E and F : from the centre B , at the distance BC , describe ( 3. Post . ) the circle CGH , and from the centre D , at the distance DG , describe the circle G KL : AL shall be equal to ...
Side 10
... produced to D and E ; the angle ABC shall be equal to the angle ACB , and the angle CBD to the angle BCE . In BD take any point F , and from AE , the greater , cut off AG equal ( 3. 1. ) to AF , the less ; also draw FC and GB ...
... produced to D and E ; the angle ABC shall be equal to the angle ACB , and the angle CBD to the angle BCE . In BD take any point F , and from AE , the greater , cut off AG equal ( 3. 1. ) to AF , the less ; also draw FC and GB ...
Andre utgaver - Vis alle
Elements of Geometry: Consisting of the First Four, and the Sixth, Books of ... Euclides Ingen forhåndsvisning tilgjengelig - 2015 |
Elements of Geometry: Consisting of the First Four, and the Sixth, Books of ... Euclides Ingen forhåndsvisning tilgjengelig - 2018 |
Elements of Geometry: Consisting of the First Four,and the Sixth, Books of ... Euclides Ingen forhåndsvisning tilgjengelig - 2013 |
Vanlige uttrykk og setninger
ABCD AC is equal adjacent angles altitudes angle ABC angle ACB angle BAC assigned base BC bisected centre circle ABC circumference cone convex surface cylinder described diameter draw drawn duplicate ratio Edition equal angles equal or equivalent equi equilateral and equiangular Euclid exterior angle fore given line given rectilineal given straight line gnomon greater Greek homologous homologous sides inscribed join Latin Let ABC measure number of sides opposite angles parallel parallelepiped parallelogram perpendicular picket plane angles prism PROB proportional proposition pyramid Q. E. D. PROP rectangle contained rectilineal figure regular polygon remaining angle right angles segment similar solid angle sphere spherical angle square of AC straight line AC THEOR touches the circle triangle ABC triangle DEF wherefore
Populære avsnitt
Side 55 - In every triangle, the square of the side subtending either of the acute angles is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle.
Side 47 - CB ; wherefore the four figures HF, CK, AG, GE are equal to the squares of AC, CB, and to twice the rectangle AC, CB : but HF, CK, AG, GE make up the whole figure ADEB, which is the square of AB: therefore the square of AB is equal to the squares of AC, CB, and twice the rectangle AC, CB. Wherefore, if a straight line, &c.
Side 12 - UPON the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity...
Side 73 - CBED is greater than a semicircle, the angles CAD, CED are equal : therefore the whole angle BAD is, equal to the whole angle BED.
Side 8 - A New Treatise on the Use of the Globes ; or, a Philosophical View of the Earth and Heavens : comprehending an Account of the Figure, Magnitude, and Motion of the Earth: with the Natural Changes of its Surface, caused by Floods, Earthquakes, &c.
Side 142 - 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 11 - ABC is therefore equal to the remaining angle ACB, which are the angles at the base of the triangle ABC : And it has also been proved that the angle FBC is equal to the angle GCB, which are the angles upon the other side of the base. Therefore, " the angles at the base
Side 53 - AB be the given straight line ; it is required to divide it 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.
Side 30 - 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 sidef. For any rectilineal figure ABCDE can be divided into as many triangles as the figure has sides, by drawing straight lines from a point F within the figure to each of its angles.
Side 9 - If two triangles have two sides of the one equal to two sides of the...