The synoptical Euclid; being the first four books of Euclid's Elements of geometry, with exercises, by S.A. Good1853 |
Dentro del libro
Página 10
... sides BF , FC are equal to the two CG , GB , each to each ; and the angle BFC is equal to the angle CGB , and the base BC is common to the two triangles BFC , CGB ; wherefore ( I. 4. ) 4. The triangles BFC , CGB , are equal , and their ...
... sides BF , FC are equal to the two CG , GB , each to each ; and the angle BFC is equal to the angle CGB , and the base BC is common to the two triangles BFC , CGB ; wherefore ( I. 4. ) 4. The triangles BFC , CGB , are equal , and their ...
Página 11
... side of the base . Therefore the angles at the base , & c . Q.E.D. COROLLARY . - Hence every equilateral triangle is ... BC common to both , 1. The two sides DB , BC , are equal to the two AC , CB , each to each ; and the angle DBC is ...
... side of the base . Therefore the angles at the base , & c . Q.E.D. COROLLARY . - Hence every equilateral triangle is ... BC common to both , 1. The two sides DB , BC , are equal to the two AC , CB , each to each ; and the angle DBC is ...
Página 13
... BC equal to the base EF . The angle BAC is equal to the angle EDF . A D G B E For if the triangle ABC be applied to ... side of it , there can be two triangles that have their sides which are terminated in one extremity of the base equal ...
... BC equal to the base EF . The angle BAC is equal to the angle EDF . A D G B E For if the triangle ABC be applied to ... side of it , there can be two triangles that have their sides which are terminated in one extremity of the base equal ...
Página 18
... side of it , ( I. 13. ) 1. The angles ABC , ABE , are together equal to two right angles ; but the angles ABC , ABD ... BC . The remaining angle ABE is equal to the remaining And in like manner it may be demonstrated that no other can be ...
... side of it , ( I. 13. ) 1. The angles ABC , ABE , are together equal to two right angles ; but the angles ABC , ABD ... BC . The remaining angle ABE is equal to the remaining And in like manner it may be demonstrated that no other can be ...
Página 19
... side BC be produced to D , the exterior angle ACD is greater than either of the interior opposite angles CBA , BAČ ... side BC be bisected , it may be demonstrated that the angle BCG that is ( I. 15. ) 6. The angle ACD is greater than ...
... side BC be produced to D , the exterior angle ACD is greater than either of the interior opposite angles CBA , BAČ ... side BC be bisected , it may be demonstrated that the angle BCG that is ( I. 15. ) 6. The angle ACD is greater than ...
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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 |