The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth : the Errors by which Theon, Or Others, Have Long Ago Vitiated These Books are Corrected, and Some of Euclid's Demonstrations are Restored : Also, the Book of Euclid's Data, in Like Manner Corrected : to this Edition are Also Annexed, Elements of Plane and Spherical TrigonometryRobert Desilver, 1821 - 516 páginas |
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Página 15
... angle BAC equal to the angle EDF , the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite , shall be equal each to each , viz . the angle ...
... angle BAC equal to the angle EDF , the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite , shall be equal each to each , viz . the angle ...
Página 18
... angle ECD is greater than the angle BCD ; wherefore the angle FDC is likewise greater than BCD ; much more than is ... BAC is equal to the angle EDF . For , if the triangle ABC be applied to DEF , so that the point B B be on E ...
... angle ECD is greater than the angle BCD ; wherefore the angle FDC is likewise greater than BCD ; much more than is ... BAC is equal to the angle EDF . For , if the triangle ABC be applied to DEF , so that the point B B be on E ...
Página 19
... angle BAC coincides with the angle EDF , and is equal ( 8. Ax . ) to it . Therefore if two triangles , & c . Q. E. D. PROP . IX . PROB . To bisect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the ...
... angle BAC coincides with the angle EDF , and is equal ( 8. Ax . ) to it . Therefore if two triangles , & c . Q. E. D. PROP . IX . PROB . To bisect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the ...
Página 24
... angles . " Let ABC be a triangle , and let its side BC be produced to D , the exterior angle ACD is greater than either of the interior op- posite angles CBA , BAC . Bisect ( 10. 1. ) AC in E , join BE and produce it to F , and make EF ...
... angles . " Let ABC be a triangle , and let its side BC be produced to D , the exterior angle ACD is greater than either of the interior op- posite angles CBA , BAC . Bisect ( 10. 1. ) AC in E , join BE and produce it to F , and make EF ...
Página 25
... BAC , ACB , as also CAB , ABC , are less than two right angles . Therefore any two angles , & c . Q.E. D. may PROP . XVIII . THEOR . THE greater side of every triangle is opposite to the greater angle ... angle ABC , is also greater than ...
... BAC , ACB , as also CAB , ABC , are less than two right angles . Therefore any two angles , & c . Q.E. D. may PROP . XVIII . THEOR . THE greater side of every triangle is opposite to the greater angle ... angle ABC , is also greater than ...
Otras ediciones - Ver todas
The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Sin vista previa disponible - 2018 |
Términos y frases comunes
AC is equal altitude angle ABC angle BAC base BC BC is given bisected centre circle ABCD circumference cone 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 gnomon greater join less Let ABC meet multiple parallel parallelogram perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment side BC similar solid angle solid parallelopipeds sphere spherical angle square of AC straight line AB straight line BC tangent THEOR third triangle ABC vertex wherefore
Pasajes populares
Página 11 - Let it be granted that a straight line may be drawn from any one point to any other point.
Página 155 - IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle...
Página 329 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Página 20 - To draw a straight line at right angles to a given straight line, from a given point in the same.
Página 9 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Página 55 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Página 53 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Página 318 - 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 21 - The angles which one straight line makes with another upon one tide of it, are either two right angles, or are together equal to two right angles. Let the straight line AB make with CD, upon one side of it the angles CBA, ABD ; these are either two right angles, or are together equal to two right angles. For, if the angle CBA be equal to ABD, each of them is a right angle (Def.
Página 27 - To construct a triangle of which the sides shall be equal to three given straight lines ; but any two whatever of these lines must be greater than the third (20.