Elements of geometry, based on Euclid, books i-iii1876 - 119 páginas |
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Página 6
... of the circle , [ and v straight line drawn from the centre to the circumference ed a radius of the circle ] . • ་ 17. A diameter of a circle is a straight line 6 GEOMETRY . Thus, the angle contained by the straight lines AB ...
... of the circle , [ and v straight line drawn from the centre to the circumference ed a radius of the circle ] . • ་ 17. A diameter of a circle is a straight line 6 GEOMETRY . Thus, the angle contained by the straight lines AB ...
Página 7
... diameter and the part of the circumference cut off by the diameter . 19. A segment of a circle is the figure contained by a straight line and the part of the circumference which it cuts off . 20. Rectilineal figures are those which are ...
... diameter and the part of the circumference cut off by the diameter . 19. A segment of a circle is the figure contained by a straight line and the part of the circumference which it cuts off . 20. Rectilineal figures are those which are ...
Página 58
... diameter , together with the two complements , is called a gnomon . Thus the parallelogram HG , to- gether with the complements AF , FC , is a gnomon , which is briefly ex- pressed by the letters AGK , or EHC , which are at the opposite ...
... diameter , together with the two complements , is called a gnomon . Thus the parallelogram HG , to- gether with the complements AF , FC , is a gnomon , which is briefly ex- pressed by the letters AGK , or EHC , which are at the opposite ...
Página 85
... diameter ; and of the rest , that which is nearer to the least is always less than one more remote ; and from the same point there can be drawn to the circumference two straight lines , and only two , which are equal to one another ...
... diameter ; and of the rest , that which is nearer to the least is always less than one more remote ; and from the same point there can be drawn to the circumference two straight lines , and only two , which are equal to one another ...
Página 86
... diameter AG , and the nearer to it shall be less than the more remote , viz . , DK less than DL , and DL less than DH . CONSTRUCTION . - Take M , the centre of the circle ABC ( III . 1 ) , and join ME , MF , MC , MH , ML , MK . H GB M ...
... diameter AG , and the nearer to it shall be less than the more remote , viz . , DK less than DL , and DL less than DH . CONSTRUCTION . - Take M , the centre of the circle ABC ( III . 1 ) , and join ME , MF , MC , MH , ML , MK . H GB M ...
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Términos y frases comunes
ABCD angle ABC angle BAC angle BCD angle EDF angle equal base BC BC is equal bisect centre chord circle ABC circumference coincide common Const CONSTRUCTION describe diagonal diameter difference divided double draw drawn equal to CD exterior angle extremities fall figure four given point given rectilineal given straight line gnomon greater impossible join length less Let ABC Let the straight manner meet opposite angles parallel parallelogram pass perpendicular possible produced PROOF PROOF.-Because proved Q. E. D. Proposition rectangle contained right angles segment semicircle shown side BC sides square on AC Take taken third touches the circle triangle ABC twice the rectangle unequal
Pasajes populares
Página 37 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are equal to two right angles.
Página 13 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal. Let ABC be an isosceles triangle, of which the side AB is equal to AC, and let the straight lines AB, AC be produced to D and E.
Página 7 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Página 17 - If two triangles have two sides of the one equal to two sides of the...
Página 53 - If the square described upon one of the sides of a triangle, be equal to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle.
Página 9 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Página 71 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Página 9 - Things which are double of the same, are equal to one another. 7. Things which are halves of the same, are equal to one another.
Página 34 - Wherefore, if a straight line, &c. QED PROPOSITION XXVIII. THEOREM. If a straight line falling upon two other straight lines, make the exterior angle equal to the interior and opposite upon the same side of the line ; or make the interior angles upon the same side together equal to two right angles ; the two straight lines shall be parallel to one another.
Página 69 - 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, together with the square of half the line bisected, is equal to the square of the straight line, which is made up of the half and the part produced.