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 47
In every parallelogram , any of the parallelograms about a diameter , together with the two complements , is called a gnomon . A E H F B " Thus the parallelogram HG , together with the complements AF , FC , is the gnomon , which is more ...
In every parallelogram , any of the parallelograms about a diameter , together with the two complements , is called a gnomon . A E H F B " Thus the parallelogram HG , together with the complements AF , FC , is the gnomon , which is more ...
Página 52
to DB ; and DF , together with CH , is the gnomon CMG ; therefore 4 . The gnomon CMG is equal to the rectangle AD , DB : to each of these add LG , which is equal ( II . 4. Cor . ) to the square of ( ' ; therefore 5 .
to DB ; and DF , together with CH , is the gnomon CMG ; therefore 4 . The gnomon CMG is equal to the rectangle AD , DB : to each of these add LG , which is equal ( II . 4. Cor . ) to the square of ( ' ; therefore 5 .
Página 53
The rectangle AD , DB , together with the square of CB , is equal to the gnomon CMG and the figure LG . But the gnomon CMG and LG make up the whole figure CEFD , which is the square of CD ; therefore 6 . The rectangle AD , DB , together ...
The rectangle AD , DB , together with the square of CB , is equal to the gnomon CMG and the figure LG . But the gnomon CMG and LG make up the whole figure CEFD , which is the square of CD ; therefore 6 . The rectangle AD , DB , together ...
Página 54
but the gnomon AKF , together with the squares CK , HF , make up the whole figure ADEB and CK , which are the squares of AB and BC ; therefore 7 . The squares of AB and BC are equal to twice the rectangle AB , BC , together with the ...
but the gnomon AKF , together with the squares CK , HF , make up the whole figure ADEB and CK , which are the squares of AB and BC ; therefore 7 . The squares of AB and BC are equal to twice the rectangle AB , BC , together with the ...
Página 55
The eight rectangles which contain the gnomon AOH , are quadruple of AK : and because AK is the rectangle contained by AB , BC , for BK is equal to BC , therefore 11 . Four times the rectangle AB , BC , is quadruple of AK ; but the ...
The eight rectangles which contain the gnomon AOH , are quadruple of AK : and because AK is the rectangle contained by AB , BC , for BK is equal to BC , therefore 11 . Four times the rectangle AB , BC , is quadruple of AK ; but the ...
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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 |