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 28
If a straight line , falling upon two other straight lines , make the alternate angles equal to one another , these two straight lines shall be parallel . Let the straight line EF , which falls upon the two straight lines AB , CD , make ...
If a straight line , falling upon two other straight lines , make the alternate angles equal to one another , these two straight lines shall be parallel . Let the straight line EF , which falls upon the two straight lines AB , CD , make ...
Página 29
Let the straight line EF fall upon the parallel straight lines AB , CD ; the alternate angles AGH , GHD , are equal to one another ; and the exterior angle EGB is equal to the interior and opposite , upon the same side , GHD ; and the ...
Let the straight line EF fall upon the parallel straight lines AB , CD ; the alternate angles AGH , GHD , are equal to one another ; and the exterior angle EGB is equal to the interior and opposite , upon the same side , GHD ; and the ...
Página 30
but those straight lines which , with another straight line falling upon them , make the interior angles on the same side less than two right angles , will meet ( Ax . 12. ) together if continually produced ; therefore 3.
but those straight lines which , with another straight line falling upon them , make the interior angles on the same side less than two right angles , will meet ( Ax . 12. ) together if continually produced ; therefore 3.
Página 31
Again , because AB is parallel to CE , and BD falls upon them , 2. The exterior angle ECD is equal to the interior and opposite angle ABC ; but the angle ACE was shown to be equal to the angle BAC ; therefore ( Ax . 2. ) 3.
Again , because AB is parallel to CE , and BD falls upon them , 2. The exterior angle ECD is equal to the interior and opposite angle ABC ; but the angle ACE was shown to be equal to the angle BAC ; therefore ( Ax . 2. ) 3.
Página 41
Then because the straight line HF falls upon the parallels AH , EF , ( I. 29. ) 1. The angles AHF , HFE , are together equal to two right angles ; wherefore ( Ax . 9. ) 2. The angles BHF , HFE , are less than two right angles ; but ( Ax ...
Then because the straight line HF falls upon the parallels AH , EF , ( I. 29. ) 1. The angles AHF , HFE , are together equal to two right angles ; wherefore ( Ax . 9. ) 2. The angles BHF , HFE , are less than two right angles ; but ( Ax ...
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The Synoptical Euclid; Being the First Four Books of Euclid's Elements of ... EUCLID.,Samuel A. GOOD Sin vista previa disponible - 1854 |
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 |