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 14
The two sides AC , CD are equal to BC , CD , each to each ; and ( Constr . ) 2. The angle ACD is equal to the angle BCD ; therefore ( I. 4. ) wherefore 4. The straight line AB is divided into two ...
The two sides AC , CD are equal to BC , CD , each to each ; and ( Constr . ) 2. The angle ACD is equal to the angle BCD ; therefore ( I. 4. ) wherefore 4. The straight line AB is divided into two ...
Página 17
At the point B , in the straight line AB , let the two straight lines BC , BD , upon the opposite sides of AB , make the adjacent angles ABC , ABD , equal together to two right angles . BD is in the same straight line with CB .
At the point B , in the straight line AB , let the two straight lines BC , BD , upon the opposite sides of AB , make the adjacent angles ABC , ABD , equal together to two right angles . BD is in the same straight line with CB .
Página 18
same straight line with it ; therefore , because the straight line AB makes angles with the straight line CBE , upon one side of it , ( I. 13. ) 1. The angles ABC , ABE , are together ... BE is not in the same straight line with BC .
same straight line with it ; therefore , because the straight line AB makes angles with the straight line CBE , upon one side of it , ( I. 13. ) 1. The angles ABC , ABE , are together ... BE is not in the same straight line with BC .
Página 19
If one side of a triangle be produced , the exterior angle is greater than either of the interior opposite angles . Let ABC be a triangle , and let its side BC be produced to D , the exterior angle ACD is greater than either of the ...
If one side of a triangle be produced , the exterior angle is greater than either of the interior opposite angles . Let ABC be a triangle , and let its side BC be produced to D , the exterior angle ACD is greater than either of the ...
Página 20
A B D Produce BC to D ; and because ACD is the exterior angle of the triangle ABC , ( I. 16. ) 1. ACD is greater than the interior and ... Let ABC be a triangle , of which the side AC is greater than the side AB ; the angle ABC is ...
A B D Produce BC to D ; and because ACD is the exterior angle of the triangle ABC , ( I. 16. ) 1. ACD is greater than the interior and ... Let ABC be a triangle , of which the side AC is greater than the side AB ; the angle ABC is ...
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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 BC bisected centre circle ABC circumference coincide common demonstrated describe diameter distance divided double draw equal angles equal Constr exterior angle extremity fall figure four given circle given point given straight line given triangle greater impossible inscribed join less Let ABC likewise manner meet opposite angles parallel parallelogram pass pentagon perpendicular point F produced Q.E.D. PROP reason rectangle contained rectilineal figure remaining angle required to describe right angles segment semicircle shown side BC sides square of AC straight line AC 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 |