The Elements of Euclid, containing the first six books, with a selection of geometrical problems. To which is added the parts of the eleventh and twelfth books which are usually read at the universities. By J. Martin1874 |
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Seite 42
... BC the given straight line . It is required to draw , through the point A , a straight line parallel to the straight line BC . E B D A F C Construction . In the line BC take any point D , and join AD ; at the point A in the straight ...
... BC the given straight line . It is required to draw , through the point A , a straight line parallel to the straight line BC . E B D A F C Construction . In the line BC take any point D , and join AD ; at the point A in the straight ...
Seite 45
... parallel . A B C D Construction . Join BC . Demonstration . Then , because AB is parallel to CD , and BC meets them , therefore 1. The angle ABC is equal to the alternate angle BCD ( Ι . 29 ) ; and because AB is equal to CD , and BC ...
... parallel . A B C D Construction . Join BC . Demonstration . Then , because AB is parallel to CD , and BC meets them , therefore 1. The angle ABC is equal to the alternate angle BCD ( Ι . 29 ) ; and because AB is equal to CD , and BC ...
Seite 46
... BC is a diameter . Then the opposite sides and angles of the figure shall be equal to one another , and the diameter BC shall bisect it . A B C D Demonstration . Because AB is parallel to CD , and BC meets them , therefore 1. The angle ...
... BC is a diameter . Then the opposite sides and angles of the figure shall be equal to one another , and the diameter BC shall bisect it . A B C D Demonstration . Because AB is parallel to CD , and BC meets them , therefore 1. The angle ...
Seite 49
... BC is equal to FG ( hyp . ) , and FG to EH ( I. 34 ) , therefore 1. BC is equal to EH ( Ax . 1 ) , and these lines ... parallel straight lines towards the same parts , are themselves equal and parallel ( I. 33 ) ; therefore ...
... BC is equal to FG ( hyp . ) , and FG to EH ( I. 34 ) , therefore 1. BC is equal to EH ( Ax . 1 ) , and these lines ... parallel straight lines towards the same parts , are themselves equal and parallel ( I. 33 ) ; therefore ...
Seite 50
... parallel to CA ( I. 31 ) ; and through C draw CF parallel to BD . Demonstration . Then and 1. Each of the figures EBCA , DBCF is a parallelogram ; 2. EBCA is equal to DBCF ( I. 35 ) , because they are upon the same base BC , and between ...
... parallel to CA ( I. 31 ) ; and through C draw CF parallel to BD . Demonstration . Then and 1. Each of the figures EBCA , DBCF is a parallelogram ; 2. EBCA is equal to DBCF ( I. 35 ) , because they are upon the same base BC , and between ...
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The Elements of Euclid, Containing the First Six Books, with a Selection of ... Euclides Keine Leseprobe verfügbar - 2016 |
Häufige Begriffe und Wortgruppen
AB is equal AC is equal adjacent angles angle ABC angle ACB angle BAC angle BCD angle DEF angle EDF angle equal base BC bisected centre circle ABC circumference constr Demonstration diameter double draw equal angles equal to F equiangular equilateral triangle equimultiples exterior angle given circle given point given straight line gnomon greater ratio inscribed less Let ABC Let the straight meet multiple opposite angle parallel to BC parallelogram perpendicular plane polygon produced proportionals PROPOSITION 13 Q.E.D. PROPOSITION rectangle contained remaining angle right angles segment similar square on AC straight line AB straight line BC straight line drawn Theorem three straight lines tiple touches the circle triangle ABC triangle DEF twice the rectangle wherefore
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Seite 1 - 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 6 - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Seite 232 - If two triangles, which have two sides of the one proportional to two sides of the other, be joined at one angle, so as to have their homologous sides parallel to one another, the remaining sides shall be in a straight line. Let...
Seite 112 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Seite 209 - ... triangles which have one angle in the one equal to one angle in the other, and their sides about the equal angles reciprocally proportional, are equal to one another.
Seite 269 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Seite 199 - 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 23 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Seite 63 - If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line and of the square on the line between the points of section. Let the straight line AB be divided into two equal parts...
Seite 32 - ... twice as many right angles as the figure has sides ; therefore all the angles of the figure together with four right angles, are equal to twice as many right angles as the figure has sides.