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 8
BC is equal to BG ; and because D is the centre of the circle GLK , 2. DL is equal to DG ; and DA , DB , parts of them are equal ( Construction ) ; therefore , ( Ax . 3. ) The remainder AL is equal to the remainder BG . 3 .
BC is equal to BG ; and because D is the centre of the circle GLK , 2. DL is equal to DG ; and DA , DB , parts of them are equal ( Construction ) ; therefore , ( Ax . 3. ) The remainder AL is equal to the remainder BG . 3 .
Página 10
Because AF is equal ( Constr . ) to AG , and AB ( Hypothesis ) to AC , the two sides FA , AC are equal to the two GA , AB , each to each ; and they contain the angle FAG common to the two triangles AFC , AGB ; therefore ( I. 4. ) 1.
Because AF is equal ( Constr . ) to AG , and AB ( Hypothesis ) to AC , the two sides FA , AC are equal to the two GA , AB , each to each ; and they contain the angle FAG common to the two triangles AFC , AGB ; therefore ( I. 4. ) 1.
Página 13
Let ABC , DEF , be two triangles having the two sides AB , AC , equal to the two sides DE , DF , each to each , viz . ... The two sides DA , AF , are equal to the two sides EA , AF , each to each ; and ( Constr . ) 2.
Let ABC , DEF , be two triangles having the two sides AB , AC , equal to the two sides DE , DF , each to each , viz . ... The two sides DA , AF , are equal to the two sides EA , AF , each to each ; and ( Constr . ) 2.
Página 14
and ( Constr . ) 2. The base DF is equal to the base EF ; therefore ( I. 8. ) 3 . wherefore The angle DAF is equal to the angle EAF ; 4. The angle BAC is bisected by the straight line AF . Which was to be done . PROP . X. - PROBLEM .
and ( Constr . ) 2. The base DF is equal to the base EF ; therefore ( I. 8. ) 3 . wherefore The angle DAF is equal to the angle EAF ; 4. The angle BAC is bisected by the straight line AF . Which was to be done . PROP . X. - PROBLEM .
Página 15
... Because DC is equal to CE , and FC common to the two triangles DCF , ECF ; The two sides DC , CF , are equal to the two EC , CF , 1 . each to each ; and ( Constr . ) 2 . therefore ( I. 8. ) The base DF is equal to the base EF ; 3.
... Because DC is equal to CE , and FC common to the two triangles DCF , ECF ; The two sides DC , CF , are equal to the two EC , CF , 1 . each to each ; and ( Constr . ) 2 . therefore ( I. 8. ) The base DF is equal to the base EF ; 3.
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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 |