The synoptical Euclid; being the first four books of Euclid's Elements of geometry, with exercises, by S.A. Good |
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In this edition , it is endeavoured , by a new , yet extremely simple , typographical arrangement , to render the text of Euclid more perspicuous than when printed in the ordinary manner , and to make it , as it were , its own ...
In this edition , it is endeavoured , by a new , yet extremely simple , typographical arrangement , to render the text of Euclid more perspicuous than when printed in the ordinary manner , and to make it , as it were , its own ...
Página 15
The angle CBE is equal to the angle EBA ; in the same manner , because ABD is a straight line , 2. The angle DBE is equal to the angle EBA ; wherefore ( Ax . 1. ) 3. The angle DBE is equal to the angle CBE , the less to the greater ...
The angle CBE is equal to the angle EBA ; in the same manner , because ABD is a straight line , 2. The angle DBE is equal to the angle EBA ; wherefore ( Ax . 1. ) 3. The angle DBE is equal to the angle CBE , the less to the greater ...
Página 18
The remaining angle ABE is equal to the remaining And in like manner it may be demonstrated that no other can be in the same straight line with it but BD , therefore 5. BD is in the same straight line with CB .
The remaining angle ABE is equal to the remaining And in like manner it may be demonstrated that no other can be in the same straight line with it but BD , therefore 5. BD is in the same straight line with CB .
Página 19
In the same manner it can be demonstrated that 5. The angles CEB , AED , are equal . Therefore , if two straight lines , & c . Q.E.D. COR . 1. - From this it is manifest , that , if two straight lines cut one another , the angles they ...
In the same manner it can be demonstrated that 5. The angles CEB , AED , are equal . Therefore , if two straight lines , & c . Q.E.D. COR . 1. - From this it is manifest , that , if two straight lines cut one another , the angles they ...
Página 20
In like manner , it may be demonstrated , that 5. BAC , ACB , as also CAB , ABC , are less than two right angles . two angles , & c . Q.E.D. PROP . XVIII . THEOREM . The greater side of every triangle is opposite to the greater angle .
In like manner , it may be demonstrated , that 5. BAC , ACB , as also CAB , ABC , are less than two right angles . two angles , & c . Q.E.D. PROP . XVIII . THEOREM . The greater side of every triangle is opposite to the greater angle .
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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 |