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
... right 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 ...
... right 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 ...
Σελίδα 26
... angle GHD ; and they are the alternate angles ; therefore AB is parallel to CD . Again , because the angles BGH , GHD are equal to two right angles ; and AGH , BGH are also d 13. 1. equal to two right angles ; the angles AGH , BGH are equal ...
... angle GHD ; and they are the alternate angles ; therefore AB is parallel to CD . Again , because the angles BGH , GHD are equal to two right angles ; and AGH , BGH are also d 13. 1. equal to two right angles ; the angles AGH , BGH are equal ...
Σελίδα 29
... angles of these triangles are Book I. equal to twice as many right angles as there are triangles , that is , as there are sides of the figure , and the same angles are equal to the angles of the figure together with the angles at the ...
... angles of these triangles are Book I. equal to twice as many right angles as there are triangles , that is , as there are sides of the figure , and the same angles are equal to the angles of the figure together with the angles at the ...
Σελίδα 39
... angles D are right angles ; because the straight E line AD meeting the parallels AB , DE , the angles BAD , ADE are equal * to two right angles ; but BAD is a right angle ; therefore also ADE is a e 29. 1 . right angle ; but the opposite ...
... angles D are right angles ; because the straight E line AD meeting the parallels AB , DE , the angles BAD , ADE are equal * to two right angles ; but BAD is a right angle ; therefore also ADE is a e 29. 1 . right angle ; but the opposite ...
Σελίδα 50
... angle ACE is a right angle , the two others AEC , EAC together d 32. 1. make one right angled ; and they are equal to one another ; each of them therefore is half a right angle . For the same E reason each of the angles CEВ , EBC is half a ...
... angle ACE is a right angle , the two others AEC , EAC together d 32. 1. make one right angled ; and they are equal to one another ; each of them therefore is half a right angle . For the same E reason each of the angles CEВ , EBC is half a ...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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...