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 18
... Q. E. D. PROP . VIII . THEOR . IF two triangles have two sides of the one equal to two sides of the other , each to each , and have likewise their bases equal ; the angle which is contained by the two sides of the one shall be equal to ...
... Q. E. D. PROP . VIII . THEOR . IF two triangles have two sides of the one equal to two sides of the other , each to each , and have likewise their bases equal ; the angle which is contained by the two sides of the one shall be equal to ...
Página 19
... 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 given rectilineal angle , it is required to bisect it . A Take any point D in AB , and from AC cut ( 3. 1 ...
... 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 given rectilineal angle , it is required to bisect it . A Take any point D in AB , and from AC cut ( 3. 1 ...
Página 24
... Q. E. D. PROP . XVII . THEOR . ANY two angles of a triangle are together less than two right angles . Let ABC be any triangle ; any two of its angles together are less than two right angles . Produce BC to D ; and because ACD is the ...
... Q. E. D. PROP . XVII . THEOR . ANY two angles of a triangle are together less than two right angles . Let ABC be any triangle ; any two of its angles together are less than two right angles . Produce BC to D ; and because ACD is the ...
Página 25
... Q.E. D. may PROP . XVIII . THEOR . THE greater side of every triangle is opposite to the greater angle . Let ABC be a triangle , of which the side AC is greater than the side AB ; the angle ABC , is also greater than the angle BCA ...
... Q.E. D. may PROP . XVIII . THEOR . THE greater side of every triangle is opposite to the greater angle . Let ABC be a triangle , of which the side AC is greater than the side AB ; the angle ABC , is also greater than the angle BCA ...
Página 26
... Q. E. D. PROP . XX . THEOR . ANY two sides of a triangle are together greater than the third side . * Let ABC be a triangle ; any two sides of it together are great- er than the third side , viz . the sides BA , AC greater than the side ...
... Q. E. D. PROP . XX . THEOR . ANY two sides of a triangle are together greater than the third side . * Let ABC be a triangle ; any two sides of it together are great- er than the third side , viz . the sides BA , AC greater than the side ...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Pré-visualização indisponível - 2018 |
Palavras e frases frequentes
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
Passagens conhecidas
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.