Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious Notes and IllustrationsA. Constable & Company, 1817 - 432 Seiten |
Im Buch
Ergebnisse 1-5 von 23
Seite 10
... be equal , when , applied to each other , they wholly coincide ; they are equivalent , if , with- out coinciding , they yet contain the same space . A PROPOSITION is a distinct portion of abstract science . 10 ELEMENTS OF GEOMETRY .
... be equal , when , applied to each other , they wholly coincide ; they are equivalent , if , with- out coinciding , they yet contain the same space . A PROPOSITION is a distinct portion of abstract science . 10 ELEMENTS OF GEOMETRY .
Seite 13
... applied to DEF : The point A being laid on D , and the side AC on DE , their other extremities C and E must coincide , since AC is equal to DE . And because AB is equal to DF , the point B must occur in the circum- ference of a circle ...
... applied to DEF : The point A being laid on D , and the side AC on DE , their other extremities C and E must coincide , since AC is equal to DE . And because AB is equal to DF , the point B must occur in the circum- ference of a circle ...
Seite 14
... applied to DEF : The ver- tex B being placed on E , and the side BA on ED , the ex- tremity A must fall upon D , since AB is equal to DE . And because the angle or divergence ABC is equal to DEF , and the side AB co- incides with DE ...
... applied to DEF : The ver- tex B being placed on E , and the side BA on ED , the ex- tremity A must fall upon D , since AB is equal to DE . And because the angle or divergence ABC is equal to DEF , and the side AB co- incides with DE ...
Seite 28
... applied to DF , the o- ther side AB must lie along DE ; and for the same reason , the an- gles BCA and EFD being equal , the side CB must lie a- long FE . Wherefore the point B , which is common to both the lines AB and CB , will be ...
... applied to DF , the o- ther side AB must lie along DE ; and for the same reason , the an- gles BCA and EFD being equal , the side CB must lie a- long FE . Wherefore the point B , which is common to both the lines AB and CB , will be ...
Seite 29
... applied to DEF , the an- gle BAC will adapt itself to EDF , since they are equal ; and the point B must coincide with E , because the side AB is equal to DE . But the other equal sides BC and EF , now stretching from the same point E ...
... applied to DEF , the an- gle BAC will adapt itself to EDF , since they are equal ; and the point B must coincide with E , because the side AB is equal to DE . But the other equal sides BC and EF , now stretching from the same point E ...
Andere Ausgaben - Alle anzeigen
Elements of Geometry, and Plane Trigonometry: With an Appendix, and Very ... University Professor Emeritus John Leslie, Sir Keine Leseprobe verfügbar - 2016 |
Häufige Begriffe und Wortgruppen
ABCD adjacent angle altitude angle ABC angle ADB angle BAC base AC bisect centre chord circle circumference consequently construction contained angle cosine decagon denote describe diameter difference distance diverging lines divided draw equal to BC equilateral triangle equivalent to twice evidently exterior angle given greater half Hence hypotenuse inscribed isosceles triangle join let fall likewise measure parallel perpendicular point G polygon PROB PROP Proposition quadrilateral figure quantities radius ratio rectangle rectangle contained rectilineal figure rhomboid right angles right-angled triangle Scholium segments semicircle semiperimeter side AC sides AB sine square of AC squares of AB straight line tangent THEOR tion triangle ABC twice the rectangle twice the square vertex vertical angle whence Wherefore
Beliebte Passagen
Seite 30 - ... if a straight line, &c. QED PROPOSITION 29. — Theorem. If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles.
Seite 333 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when any...
Seite 294 - If a straight line meets two straight lines, so as to " make the two interior angles on the same side of it taken " together less than two right angles...
Seite 10 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Seite 137 - Componendo, by composition ; when there are four proportionals, and it is inferred that the first together with the second, is to the second, as the third together with the fourth, is to the fourth.
Seite 84 - The angle at the centre of a circle is double of the angle at the circumference upon the same base, that is, upon the same part of the circumference.
Seite 292 - Thus, for" example, he to whom the geometrical proposition, that the angles of a triangle are together equal to two right angles...
Seite 93 - UPON a given straight line to describe a segment of a circle containing an angle equal to a given rectilineal angle.
Seite 38 - 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.
Seite 58 - The rectangle contained by the sum and difference of two straight lines is equivalent to the difference of the squares of these lines.