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 sider |
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Side 14
... wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC . Wherefore from the given point A a straight line AL has been drawn equal ...
... wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC . Wherefore from the given point A a straight line AL has been drawn equal ...
Side 15
... wherefore also the point C shall coincide with the point F , because the straight line AC is equal to DF : but the point B coincides with the point E ; wherefore the base BC shall coincide with the base EF , because the point B ...
... wherefore also the point C shall coincide with the point F , because the straight line AC is equal to DF : but the point B coincides with the point E ; wherefore the base BC shall coincide with the base EF , because the point B ...
Side 19
... wherefore likewise 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 ...
... wherefore likewise 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 ...
Side 31
... wherefore also the angle BCG is equal to the angle BCA , the less to the greater , which is impossible ; therefore ... wherefore BC is not unequal to EF , that is , it is equal to it ; and AB is equal to DE ; therefore the two AB , BC ...
... wherefore also the angle BCG is equal to the angle BCA , the less to the greater , which is impossible ; therefore ... wherefore BC is not unequal to EF , that is , it is equal to it ; and AB is equal to DE ; therefore the two AB , BC ...
Side 40
... Wherefore triangles , & c . Q. E. D. PROP . XXXVIII . THEOR . TRIANGLES upon equal bases , and between the same parallels , are equal to one another . Let the triangles ABC , DEF be upon equal bases BC , EF , and between the same ...
... Wherefore triangles , & c . Q. E. D. PROP . XXXVIII . THEOR . TRIANGLES upon equal bases , and between the same parallels , are equal to one another . Let the triangles ABC , DEF be upon equal bases BC , EF , and between the same ...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2018 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 11 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 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...
Side 329 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Side 20 - To draw a straight line at right angles to a given straight line, from a given point in the same.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.