The Elements of geometry; or, The first six books, with the eleventh and twelfth, of Euclid, with corrections, annotations, and exercises, by R. Wallace. Cassell's ed1855 |
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Seite 6
... Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one another . IX . The whole is greater than its part . Dr. Thomson , in his edition of Euclid , has added to this axiom , another ...
... Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one another . IX . The whole is greater than its part . Dr. Thomson , in his edition of Euclid , has added to this axiom , another ...
Seite 48
... magnitudes . Therefore the square of CD and twice the rectangle A C. CD are together equal to four times the rectangle A B. BC . To these equals add the square of AC . Therefore the squares of AC and CD , and twice the rectangle AC . CD ...
... magnitudes . Therefore the square of CD and twice the rectangle A C. CD are together equal to four times the rectangle A B. BC . To these equals add the square of AC . Therefore the squares of AC and CD , and twice the rectangle AC . CD ...
Seite 55
... , that point is within the circle ; and if a point be taken beyond the circumference , it is without the circle . This axiom is tacitly assumed by Euclid in this Book . II . If two magnitudes be doubles of two other BOOK III . AXIOMS . 55.
... , that point is within the circle ; and if a point be taken beyond the circumference , it is without the circle . This axiom is tacitly assumed by Euclid in this Book . II . If two magnitudes be doubles of two other BOOK III . AXIOMS . 55.
Seite 56
Euclides Robert Wallace. II . If two magnitudes be doubles of two other magnitudes , each of cach , the sum of the first two is double the sum of the other two . III . If two magnitudes be doubles of two other magnitudes , each of each ...
Euclides Robert Wallace. II . If two magnitudes be doubles of two other magnitudes , each of cach , the sum of the first two is double the sum of the other two . III . If two magnitudes be doubles of two other magnitudes , each of each ...
Seite 97
... magnitudes of the same kind to one another , in respect of quantity , is called their , ratio . The term ratio is employed to express the relation of two like magnitudes to each other , whether they be commensurable or incommensurable ...
... magnitudes of the same kind to one another , in respect of quantity , is called their , ratio . The term ratio is employed to express the relation of two like magnitudes to each other , whether they be commensurable or incommensurable ...
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The Elements of Geometry: Or, the First Six Books, with the Eleventh and ... Euclides Keine Leseprobe verfügbar - 2016 |
Häufige Begriffe und Wortgruppen
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angle DEF angle EDF base BC bisected centre circle ABC circumference cone cylinder described diagonal diameter draw duplicate ratio equal angles equal Ax equal Const equiangular equimultiples Euclid ex æquali Exercise exterior angle fore given straight line gnomon homologous sides inscribed join less meet multiple opposite angle parallelogram parallelogram AC parallelopiped pentagon perpendicular polygon prism produced proposition Q. E. D. PROP reciprocally proportional rectangle contained rectilineal figure remaining angle right angles segment similar triangles solid angle sphere squares of AC straight line drawn straight lines A B THEOREM third three plane angles three straight lines triangle ABC triangle DEF triplicate ratio twice the rectangle vertex Wherefore whole angle
Beliebte Passagen
Seite 23 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Seite 34 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Seite 2 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Seite 122 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Seite 5 - LET it be granted that a straight line may be drawn from any one point to any other point.
Seite 3 - 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 135 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar.
Seite 20 - PROBLEM. At a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle.
Seite 147 - Similar solid figures are such as have all their solid angles equal, each to each, and are contained by the same number of similar planes.
Seite 37 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square...