The synoptical Euclid; being the first four books of Euclid's Elements of geometry, with exercises, by S.A. Good |
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Página 7
Let AB be the given straight line ; it is required to describe an equilateral triangle upon it . From the centre 4 , at the distance AB , describe ... E و Because the point A is the centre of the circle BCD , ( Definition 15. ) 1 .
Let AB be the given straight line ; it is required to describe an equilateral triangle upon it . From the centre 4 , at the distance AB , describe ... E و Because the point A is the centre of the circle BCD , ( Definition 15. ) 1 .
Página 8
Euclides Samuel A Good. Because the point B is the centre of the circle CGH , ( Def . 15. ) 1 . ... Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC . Which was to be done . PROP .
Euclides Samuel A Good. Because the point B is the centre of the circle CGH , ( Def . 15. ) 1 . ... Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC . Which was to be done . PROP .
Página 13
To bisect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given rectilineal angle , it is required to bisect it . Take any point D'in AB , and from 8C cut ( I. 3. ) off AE equal to AD ; join DE ...
To bisect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given rectilineal angle , it is required to bisect it . Take any point D'in AB , and from 8C cut ( I. 3. ) off AE equal to AD ; join DE ...
Página 14
The straight line AB is divided into two equal parts in the point D. Which was to be done . PROP . XI . - PROBLEM . To draw a straight line at right angles to a given straight line , from a given point in the same . Let AB be a given ...
The straight line AB is divided into two equal parts in the point D. Which was to be done . PROP . XI . - PROBLEM . To draw a straight line at right angles to a given straight line , from a given point in the same . Let AB be a given ...
Página 15
straight line FC drawn from the given point C is at right angles to the given straight line AB F А с E B Because DC is equal CE , and FC common to the two triangles DCF , ECF ; 1 . The two sides DC , CF , are equal to the two EC ...
straight line FC drawn from the given point C is at right angles to the given straight line AB F А с E B Because DC is equal CE , and FC common to the two triangles DCF , ECF ; 1 . The two sides DC , CF , are equal to the two EC ...
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Términos y frases comunes
ABCD AC is equal AF is equal angle ABC angle ACB angle BAC angle BCD angle equal base base BC bisected centre circle ABC circumference coincide common demonstrated describe diameter distance divided double draw equal angles exterior angle extremity fall figure four given circle given point given straight line given triangle gnomon greater impossible inscribed join less Let ABC likewise manner meet opposite angles parallel parallelogram pass pentagon perpendicular point F PROBLEM produced Q.E.D. PROP reason rectangle contained rectilineal figure remaining angle required to describe right angles segment semicircle shown sides square of AC straight line AC THEOREM touches the circle triangle ABC twice the rectangle wherefore whole
Pasajes populares
Página 26 - 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. either the sides adjacent to the equal...
Página 22 - If from the ends of a side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle.
Página 32 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Página 1 - A plane superficies is that in which any two points being taken, the straight line between them lies wholly in that superficies. vm. "A plane angle is the inclination of two lines to one another in a plane, which meet together, but are not in the same direction.
Página 97 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Página 7 - AB; but things which are equal to the same are equal to one another...
Página 14 - To bisect 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 intotwo equal parts.
Página 53 - IF a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part.
Página 41 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Página 52 - 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...
Información bibliográfica
| Título | The synoptical Euclid; being the first four books of Euclid's Elements of geometry, with exercises, by S.A. Good |
| Autor | Euclides |
| Editor | Samuel A Good |
| Publicado | 1853 |
| Procedencia del original | Universidad de Oxford |
| Digitalizado | 7 Sep. 2006 |
| Exportar cita | BiBTeX EndNote RefMan |