The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and TwelfthBell & Bradfute, 1835 - 513 sider |
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Side 8
... angle BAC equal to the angle EDF ; the base BC shall be equal to the base EF ; and the triangle ABC to the tri ... remaining angles of the other , and be equal to them , viz . the angle ABC to the angle DEF , and the angle ACB to DFE ...
... angle BAC equal to the angle EDF ; the base BC shall be equal to the base EF ; and the triangle ABC to the tri ... remaining angles of the other , and be equal to them , viz . the angle ABC to the angle DEF , and the angle ACB to DFE ...
Side 9
... angle FAG com- mon to the two triangles AFC , AGB ; therefore the base FC is equal to the base GB , and the tri- angle AFC to the triangle AGB ; and the remaining angles of the one are equal to the remaining angles of the other , each ...
... angle FAG com- mon to the two triangles AFC , AGB ; therefore the base FC is equal to the base GB , and the tri- angle AFC to the triangle AGB ; and the remaining angles of the one are equal to the remaining angles of the other , each ...
Side 16
... 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 , the remaining angle ABE is equal to the remaining angle ...
... 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 , the remaining angle ABE is equal to the remaining angle ...
Side 17
... angle is greater than either of the interior opposite angles . Let ABC be a triangle , and let its side BC be ... remaining angles to the remaining angles , each to each , to which the equal sides are opposite ; wherefore the angle BAE ...
... angle is greater than either of the interior opposite angles . Let ABC be a triangle , and let its side BC be ... remaining angles to the remaining angles , each to each , to which the equal sides are opposite ; wherefore the angle BAE ...
Side 26
... angles BGH , GHD : Take away the common angle BGH , therefore the remaining angle AGH is equal to the remaining angle GHD ; and they are alternate angles ; there- fore AB is parallel to CD . Wherefore , " if a straight line , " & c ...
... angles BGH , GHD : Take away the common angle BGH , therefore the remaining angle AGH is equal to the remaining angle GHD ; and they are alternate angles ; there- fore AB is parallel to CD . Wherefore , " if a straight line , " & c ...
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The Elements Of Euclid: Viz. The First Six Books, Together With The Eleventh ... Robert Simson,Euclid,John Davidson Ingen forhåndsvisning - 2019 |
Almindelige termer og sætninger
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
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Side 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.
Side 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.
Side 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.
Side 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...
Side 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.
Side 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.
Side 30 - And because the angle ABC is equal to the angle BCD, and the angle CBD to the angle ACB...
Side 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.
Side 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.
Side 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...