The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and TwelfthBell & Bradfute, 1835 - 513 páginas |
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Página 35
... diameter AC divides it into two equal parts ; wherefore A B DE a 37. 1 . b 34. 1 . C ABCD is also double the triangle EBC . Therefore , " if a parallelogram , " & c . Q. E. D. PROP . XLII . PROB . To describe a parallelogram that shall ...
... diameter AC divides it into two equal parts ; wherefore A B DE a 37. 1 . b 34. 1 . C ABCD is also double the triangle EBC . Therefore , " if a parallelogram , " & c . Q. E. D. PROP . XLII . PROB . To describe a parallelogram that shall ...
Página 36
... diameter of any parallelogram , are equal to one another . A H D K E F Let ABCD be a parallelogram , of which the diameter is AC , let EH , FG be the pa- rallelograms about AC , that is , through which AC passes , and let BK , KD be the ...
... diameter of any parallelogram , are equal to one another . A H D K E F Let ABCD be a parallelogram , of which the diameter is AC , let EH , FG be the pa- rallelograms about AC , that is , through which AC passes , and let BK , KD be the ...
Página 45
... Wherefore , " if a straight line , ” & c . Q. E. D. COR . From the demonstration , it is manifest , that the pa- rallelograms about the diameter of a square are likewise squares . Book II . a 46. 1 . b 31. 1 OF EUCLID . 45.
... Wherefore , " if a straight line , ” & c . Q. E. D. COR . From the demonstration , it is manifest , that the pa- rallelograms about the diameter of a square are likewise squares . Book II . a 46. 1 . b 31. 1 OF EUCLID . 45.
Página 57
... diameters are equal , or Book III . from the centres of which the straight lines to the circumfe- rences are equal . This is not a definition but a theorem , the truth of which is evident ; for if the circles be applied to one another ...
... diameters are equal , or Book III . from the centres of which the straight lines to the circumfe- rences are equal . This is not a definition but a theorem , the truth of which is evident ; for if the circles be applied to one another ...
Página 63
... diameter of a circle which is not the centre , of all the straight lines which can be drawn from it to the circumference , the great- est is that in which the centre is , and the other part of that diameter is the least ; and , of any ...
... diameter of a circle which is not the centre , of all the straight lines which can be drawn from it to the circumference , the great- est is that in which the centre is , and the other part of that diameter is the least ; and , of any ...
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The Elements Of Euclid: Viz. The First Six Books, Together With The Eleventh ... Robert Simson,Euclid,John Davidson Sin vista previa disponible - 2019 |
Términos y frases comunes
ABC is given altitude angle ABC angle BAC arch base BC BC is equal bisected Book XI centre circle ABCD circumference cone cosine 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 gles gnomon greater half the perimeter hypotenuse join less Let ABC multiple parallel parallelogram perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius rectangle CB rectangle contained rectilineal figure remaining angle right angles segment side BC similar sine solid angle solid parallelepiped spherical angle square of AC straight line AB straight line BC tangent THEOR tiple triangle ABC vertex wherefore
Pasajes populares
Página 47 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced. Let the straight line AB be bisected in C, and produced to D : the rectangle AD, DB, together with the square of CB, shall be equal to the square of CD.
Página 306 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
Página 26 - if a straight line," &c. QED PROP. XXIX. THEOR. See the Jf a straight line fall upon two parallel straight ti?isepropo- 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.
Página 54 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the...
Página 170 - EQUIANGULAR parallelograms have to one another the ratio which is compounded of the ratios of their sides.* Let AC, CF be equiangular parallelograms, having the angle BCD equal to the angle ECG : the ratio of the parallelogram AC to the parallelogram CF, is the same with the ratio which is compounded of the ratios of their sides. • See Note. Let BG, CG, be placed in a straight line ; therefore DC and CE are also in a straight line (14.
Página 153 - 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.
Página 30 - And because the angle ABC is equal to the angle BCD, and the angle CBD to the angle ACB...
Página 28 - 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.
Página 64 - ... than the more remote: but of those which fall upon the convex circumference, the least is that between the point without the circle and the diameter; and, of the rest, that which is nearer to the least is always less than the more remote: and only two equal straight lines can be drawn from the point into the circumference, one upon each side of the least.
Página 5 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...