Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement of the Quadrature of the Circle and the Geometry of Solids |
Inni boken
Resultat 1-5 av 44
Side 8
Defi . is equal to AB ; and because the point B is the centre of the nition . circle
ACE , BC is equal to BA : but it has been proved that CA is equal to AB ; therefore
CA , CB are each of them d 1. Axi- equal to one anotherd ; therefore CA is equal
to ...
Defi . is equal to AB ; and because the point B is the centre of the nition . circle
ACE , BC is equal to BA : but it has been proved that CA is equal to AB ; therefore
CA , CB are each of them d 1. Axi- equal to one anotherd ; therefore CA is equal
to ...
Side 11
Ax . to the remainder CG ; and FC was proved to be equal to GB , therefore the
wo sides . BF , FC are equal to the two CG , GB , each to each ; but the angle BFC
is equal to the angle CGB ; wherefore the triangles BFC , CGB are equalb , and ...
Ax . to the remainder CG ; and FC was proved to be equal to GB , therefore the
wo sides . BF , FC are equal to the two CG , GB , each to each ; but the angle BFC
is equal to the angle CGB ; wherefore the triangles BFC , CGB are equalb , and ...
Side 12
Book 1. the whole ACF , and the part CBG to the part BCF , the remaining angle
ABC is therefore equal to the remaining angle ACB , which are the angles at the
base of the triangle ABC : and it has also been proved , that the angle FBC is ...
Book 1. the whole ACF , and the part CBG to the part BCF , the remaining angle
ABC is therefore equal to the remaining angle ACB , which are the angles at the
base of the triangle ABC : and it has also been proved , that the angle FBC is ...
Side 13
... wherefore the angle FDC is likewise greater than BCD ; much more then is the
angle BDC greater than the angle BCD . A. -В gain , because CB is equal to DB ,
the angle BDC is equal to the angle BCD ; but BDC has Book I. been proved to ...
... wherefore the angle FDC is likewise greater than BCD ; much more then is the
angle BDC greater than the angle BCD . A. -В gain , because CB is equal to DB ,
the angle BDC is equal to the angle BCD ; but BDC has Book I. been proved to ...
Side 14
Book I. been proved to be greater than the same BCD ; which is im- , possible .
The case in which the vertex of one triangle is upon a side of the other , needs no
demonstration . Therefore , upon the same base , and on the same side of it ...
Book I. been proved to be greater than the same BCD ; which is im- , possible .
The case in which the vertex of one triangle is upon a side of the other , needs no
demonstration . Therefore , upon the same base , and on the same side of it ...
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Vanlige uttrykk og setninger
ABC is equal ABCD altitude angle ABC angle ACB angle BAC arch base bisected Book centre circle circle ABC circumference coincide common compounded contained cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular equilateral equimultiples exterior angle extremities fall figure fore fourth given straight line greater half inscribed interior join less Let ABC magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism PROB produced proportional proposition proved pyramid Q. E. D. PROP ratio reason rectangle contained rectilineal figure right angles segment shown sides similar solid space square taken THEOR third triangle ABC wherefore whole
Populære avsnitt
Side 121 - 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...
Side 42 - 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.
Side 63 - Therefore, in obtuse-angled triangles, &c. QED PROP. XIII. THEOREM. In every triangle, the square of the side subtending either of the acute angles is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle.
Side 3 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Side 183 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. Let AC, CF be equiangular parallelograms having the angle BCD equal to the angle ECG ; the ratio of the parallelogram AC to the parallelogram CF is the same with the ratio which is compounded •f the ratios of their sides.
Side 3 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Side 291 - 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.
Side 160 - ... extremities of the base shall have the same ratio which the other sides of the triangle have to one...
Side 10 - ... shall be greater than the base of the other. Let ABC, DEF be two triangles, which have the two sides AB, AC, equal to the two DE, DF, each to each, viz.
Side 14 - Therefore, upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extretnity equal to one another.
Bibliografisk informasjon
| Tittel | Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement of the Quadrature of the Circle and the Geometry of Solids |
| Forfatter | John Playfair |
| Utgiver | F. Nichols, 1806 |
| Original fra | University of Michigan |
| Digitalisert | 16. feb 2008 |
| ISBN | 0608378402, 9780608378404 |
| Lengde | 311 sider |
| Eksporter sitat | BiBTeX EndNote RefMan |