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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Side 11
... fore the remaining angle ABC is 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 ...
... fore the remaining angle ABC is 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 12
... fore the angle ADC is greater also than BCD ; much more then is the angle BDC greater than the angle BCD . Again , be- cause CB is equal to DB , the angle BDC is A equal ( 5. 1. ) to the angle BCD ; but it has been demonstrated to be ...
... fore the angle ADC is greater also than BCD ; much more then is the angle BDC greater than the angle BCD . Again , be- cause CB is equal to DB , the angle BDC is A equal ( 5. 1. ) to the angle BCD ; but it has been demonstrated to be ...
Side 20
... ; therefore AC is greater than AB . Where- fore the greater angle , & c . Q. E. D. PROP . XX . THEOR . ANY two sides of a triangle are together greater than the third side . Let ABC be a triangle ; any two sides of 20 EUC . B. I. ELEMENTS.
... ; therefore AC is greater than AB . Where- fore the greater angle , & c . Q. E. D. PROP . XX . THEOR . ANY two sides of a triangle are together greater than the third side . Let ABC be a triangle ; any two sides of 20 EUC . B. I. ELEMENTS.
Side 24
... fore the angle BAC is greater than the angle EDF . fore if two angles , & c . Q. E. D. PROP . XXVI . THEOR . IF two triangles have 24 EUC . B. I. ELEMENTS.
... fore the angle BAC is greater than the angle EDF . fore if two angles , & c . Q. E. D. PROP . XXVI . THEOR . IF two triangles have 24 EUC . B. I. ELEMENTS.
Side 26
... fore BC is not unequal to EF , that is , it is equal to it ; and AB is equal to DE : therefore the two , AB , BC are equal to the two DE , EF , each to each ; and they contain equal angles : wherefore the base AC is equal to the base DF ...
... fore BC is not unequal to EF , that is , it is equal to it ; and AB is equal to DE : therefore the two , AB , BC are equal to the two DE , EF , each to each ; and they contain equal angles : wherefore the base AC is equal to the base DF ...
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...