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 12
... given rectilineal angle ; that is , to divide it into two equal angles . Let ... straight line AF bisects the angle BAC . AD . Because AD is equal ( Const ... given rectilineal angle B BAC is bisected by the straight line AF . Q. E. F. T ...
... given rectilineal angle ; that is , to divide it into two equal angles . Let ... straight line AF bisects the angle BAC . AD . Because AD is equal ( Const ... given rectilineal angle B BAC is bisected by the straight line AF . Q. E. F. T ...
Seite 13
... a given finite straight line ; that is , to divide it into two equal parts . Let AB be the given straight line . It is required to divide it into two equal parts . Describe upon AB ( I. 1 ) an equilateral triangle ABC , and bisect ( I ...
... a given finite straight line ; that is , to divide it into two equal parts . Let AB be the given straight line . It is required to divide it into two equal parts . Describe upon AB ( I. 1 ) an equilateral triangle ABC , and bisect ( I ...
Seite 14
Euclides Robert Wallace. Because ABC is a straight line , the angle CBE is equal ( Def . 10 ) to the angle EBA ... given straight line , to draw a straight line which shall make a right angle with it . 2. In a straight line of unlimited ...
Euclides Robert Wallace. Because ABC is a straight line , the angle CBE is equal ( Def . 10 ) to the angle EBA ... given straight line , to draw a straight line which shall make a right angle with it . 2. In a straight line of unlimited ...
Seite 18
... a point without a given straight line , any number of straight lines be drawn to meet it ; of all these straight lines , that which is perpendicular to the given straight line is the least ; and of others that which is nearer to the ...
... a point without a given straight line , any number of straight lines be drawn to meet it ; of all these straight lines , that which is perpendicular to the given straight line is the least ; and of others that which is nearer to the ...
Seite 19
... given points on the same side of a straight line given in position , to draw two straight lines which shall meet at a point in it , and which taken together shall be less than the sum of two straight lines drawn from the same points to ...
... given points on the same side of a straight line given in position , to draw two straight lines which shall meet at a point in it , and which taken together shall be less than the sum of two straight lines drawn from the same points to ...
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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
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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...