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 49
... gnomon . A Thus the parallelogram HG , ' together with the complements ' AF , FC , is the gnomon , which ' is more briefly expressed by the H L " letters AGK , or EHC , which are at the opposite angles of the parallelograms which make ...
... gnomon . A Thus the parallelogram HG , ' together with the complements ' AF , FC , is the gnomon , which ' is more briefly expressed by the H L " letters AGK , or EHC , which are at the opposite angles of the parallelograms which make ...
Página 53
... gnomon CMG ; therefore the gnomon CMG is equal to the rectangle AD , DB : to each of these add LG , which is equal ( 43. 1. ) to the square of CD ; therefore the gnomon CMG , together with LG , is equal to the rectangle AD , DB ...
... gnomon CMG ; therefore the gnomon CMG is equal to the rectangle AD , DB : to each of these add LG , which is equal ( 43. 1. ) to the square of CD ; therefore the gnomon CMG , together with LG , is equal to the rectangle AD , DB ...
Página 54
... gnomon CMG and the figure LG : but the gnomon CMG and LG make up the whole figure CEFD , which is the square of CD ; therefore the rectangle AD , DB , together with the square of CB , is equal to the square of CD . Where- fore , if a ...
... gnomon CMG and the figure LG : but the gnomon CMG and LG make up the whole figure CEFD , which is the square of CD ; therefore the rectangle AD , DB , together with the square of CB , is equal to the square of CD . Where- fore , if a ...
Página 55
... gnomon AKF , together with the square CK ; therefore the gnomon AKF , together with the square CK , is double H of AK : but twice the rectangle AB , BC is double of AK , for BK is equal ( Cor . 4.2 . ) to BC : therefore the gnomon ...
... gnomon AKF , together with the square CK ; therefore the gnomon AKF , together with the square CK , is double H of AK : but twice the rectangle AB , BC is double of AK , for BK is equal ( Cor . 4.2 . ) to BC : therefore the gnomon ...
Página 56
... gnomon AOH was demonstrated to be quadruple of AK : therefore four times the rectangle AB , BC is equal to the gno ... gnomon AOH and the square XH : but the gnomon AOH and XH make up the figure AEFD , which is the square of AD ...
... gnomon AOH was demonstrated to be quadruple of AK : therefore four times the rectangle AB , BC is equal to the gno ... gnomon AOH and the square XH : but the gnomon AOH and XH make up the figure AEFD , which is the square of AD ...
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.