The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and TwelfthBell & Bradfute, 1835 - 513 pages |
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Page 145
... the whole is to the greater segment , as the greater segment is to the less . IV . The altitude of any figure is the straight line drawn from its vertex perpendicu- lar to the base . K Book VI . See N. a 38. 1 . PROP.
... the whole is to the greater segment , as the greater segment is to the less . IV . The altitude of any figure is the straight line drawn from its vertex perpendicu- lar to the base . K Book VI . See N. a 38. 1 . PROP.
Page 146
... altitude are one to another as their bases . Let the triangles ABC , ACD , and the parallelograms EC , CF have the same altitude , viz . the perpendicular drawn from the point A to BD ; Then , as the base BC is to the base CD ; so is ...
... altitude are one to another as their bases . Let the triangles ABC , ACD , and the parallelograms EC , CF have the same altitude , viz . the perpendicular drawn from the point A to BD ; Then , as the base BC is to the base CD ; so is ...
Page 147
... altitudes , are one to another as their bases . Let the figures be placed so as to have their bases in the same ... altitude , viz . the perpendicular drawn from the point E to AB , they are to one another as their bases ; and for ...
... altitudes , are one to another as their bases . Let the figures be placed so as to have their bases in the same ... altitude , viz . the perpendicular drawn from the point E to AB , they are to one another as their bases ; and for ...
Page 219
... the See N. same altitude , the insisting straight lines of which are terminated in the same straight lines , in the plane opposite to the base , are equal to one another . Book XI . See the figures below . Let the OF EUCLID . 219.
... the See N. same altitude , the insisting straight lines of which are terminated in the same straight lines , in the plane opposite to the base , are equal to one another . Book XI . See the figures below . Let the OF EUCLID . 219.
Page 220
... altitude , and let their insisting straight lines AF , AG , LM , LN be terminated in the same straight line FN , and CD , CE , BH , BK be terminated in the same straight line DK ; the solid AH is equal to the solid AK . First , Let the ...
... altitude , and let their insisting straight lines AF , AG , LM , LN be terminated in the same straight line FN , and CD , CE , BH , BK be terminated in the same straight line DK ; the solid AH is equal to the solid AK . First , Let the ...
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The Elements Of Euclid: Viz. The First Six Books, Together With The Eleventh ... Robert Simson,Euclid,John Davidson No preview available - 2019 |
Common terms and phrases
ABC is given ABCD altitude angle ABC angle BAC arch base BC BC is equal bisected Book XI centre circle ABC 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
Popular passages
Page 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.
Page 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.
Page 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.
Page 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...
Page 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.
Page 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.
Page 30 - And because the angle ABC is equal to the angle BCD, and the angle CBD to the angle ACB...
Page 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.
Page 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.
Page 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...