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 Seiten |
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Seite 153
... greater segment , as the greater segment is to the less . IV . The altitude of any figure is the straight line drawn from its vertex perpendicular to the base . * See Note . U PROP . I. THEOR . TRIANGLES and parallelograms of the THE ...
... greater segment , as the greater segment is to the less . IV . The altitude of any figure is the straight line drawn from its vertex perpendicular to the base . * See Note . U PROP . I. THEOR . TRIANGLES and parallelograms of the THE ...
Seite 154
... altitude are one to another as their bases . * Let the triangles ABC , ACD , and the parallelograms EC , CF , have the same altitude , viz . the perpendicular drawn from the point A to BD : then , as the base BC is to the base CD , so ...
... altitude are one to another as their bases . * Let the triangles ABC , ACD , and the parallelograms EC , CF , have the same altitude , viz . the perpendicular drawn from the point A to BD : then , as the base BC is to the base CD , so ...
Seite 155
... altitudes , are one to another as their bases . Let the figures be placed so as to have their bases in the same ... altitude , viz . the perpendicular drawn from the point E to AB , they are to one another as their bases ; and for ...
... altitudes , are one to another as their bases . Let the figures be placed so as to have their bases in the same ... altitude , viz . the perpendicular drawn from the point E to AB , they are to one another as their bases ; and for ...
Seite 227
... altitude , the insisting lines of which are terminated in the same straight lines in the plane opposite to the base , are equal to one another . * Let the solid parallelopipeds AH , AK be upon the same base AB , and of the same altitude ...
... altitude , the insisting lines of which are terminated in the same straight lines in the plane opposite to the base , are equal to one another . * Let the solid parallelopipeds AH , AK be upon the same base AB , and of the same altitude ...
Seite 229
... altitude , the insisting straight lines of which are not terminated in the same straight lines in the plane opposite to the base , are equal to one another . * Let the parallelopipeds CM , CN be upon the same base AB , and of the same ...
... altitude , the insisting straight lines of which are not terminated in the same straight lines in the plane opposite to the base , are equal to one another . * Let the parallelopipeds CM , CN be upon the same base AB , and of the same ...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Keine Leseprobe verfügbar - 2018 |
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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
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Seite 11 - Let it be granted that a straight line may be drawn from any one point to any other point.
Seite 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...
Seite 329 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Seite 20 - To draw a straight line at right angles to a given straight line, from a given point in the same.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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.