The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and TwelfthBell & Bradfute, 1835 - 513 σελίδες |
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Σελίδα 15
... angles , or are together equal to two right angles . For if the angle CBA be equal to ABD , each of them is a A E A D C B D B C right angle ; but , if not , from the point B draw BE at right a Def . 10 . angles to CD ; therefore the ...
... angles , or are together equal to two right angles . For if the angle CBA be equal to ABD , each of them is a A E A D C B D B C right angle ; but , if not , from the point B draw BE at right a Def . 10 . angles to CD ; therefore the ...
Σελίδα 16
... angles ABC , ABE are together equala to two right angles ; but the angles ABC , ABD are likewise together equal to two right angles ; therefore the angles CBA , ABE are equal to the angles CBA , ABD : Take away the common angle ABC ...
... angles ABC , ABE are together equala to two right angles ; but the angles ABC , ABD are likewise together equal to two right angles ; therefore the angles CBA , ABE are equal to the angles CBA , ABD : Take away the common angle ABC ...
Σελίδα 17
... angles CBA , BAС . Book I. Bisect AC in E , join a 10. 1 . BE and produce it to F , A and make EF equal to BE ; F join also FC , and produce AC to G. Because AE is equal to EC , and BE to EF ; AE , E EB are equal to CE , EF , each to ...
... angles CBA , BAС . Book I. Bisect AC in E , join a 10. 1 . BE and produce it to F , A and make EF equal to BE ; F join also FC , and produce AC to G. Because AE is equal to EC , and BE to EF ; AE , E EB are equal to CE , EF , each to ...
Σελίδα 23
... equal to it , or less ; Book I. a 4. 1 . b 24. 1 . 414 but the angle BAC is not equal to the angle EDF , because ... angles of one equal to two angles of the other , each to each ; and one side equal to one side , viz . either the ...
... equal to it , or less ; Book I. a 4. 1 . b 24. 1 . 414 but the angle BAC is not equal to the angle EDF , because ... angles of one equal to two angles of the other , each to each ; and one side equal to one side , viz . either the ...
Σελίδα 24
... equal to the angle DEF ; therefore the base GC is equal to the base DF , and the triangle GBC to the triangle DEF , and the other angles to the other angles , each to each , to which the equal sides are opposite ; therefore the angle ...
... equal to the angle DEF ; therefore the base GC is equal to the base DF , and the triangle GBC to the triangle DEF , and the other angles to the other angles , each to each , to which the equal sides are opposite ; therefore the angle ...
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The Elements Of Euclid: Viz. The First Six Books, Together With The Eleventh ... Robert Simson,Euclid,John Davidson Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2019 |
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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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 30 - And because the angle ABC is equal to the angle BCD, and the angle CBD to the angle ACB...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...