Elements of geometry, based on Euclid, books i-iii1876 - 119 páginas |
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Página 95
... circle , from the extremity of it , touches the circle ( III . Def . 2 ) ; and that it touches it only in one point , because if it did meet the circle in two points it would fall within it ( III . 2 ) . Also it is evident that there ...
... circle , from the extremity of it , touches the circle ( III . Def . 2 ) ; and that it touches it only in one point , because if it did meet the circle in two points it would fall within it ( III . 2 ) . Also it is evident that there ...
Página 96
... circle , from the extremity of it , touches the circle ( III . 16 , cor . ) ; Therefore AB touches the circle , and it is drawn from the the circle . given point A. If not , sup- pose FG perpendi cular . Then must Next , let the given ...
... circle , from the extremity of it , touches the circle ( III . 16 , cor . ) ; Therefore AB touches the circle , and it is drawn from the the circle . given point A. If not , sup- pose FG perpendi cular . Then must Next , let the given ...
Página 97
... circle shall be in that line . Let the straight line DE touch the circle ABC in C , and from C let CA be drawn at ... touches the circle ABC , and FC is drawn from the assumed centre to the point of contact , Therefore FC is ...
... circle shall be in that line . Let the straight line DE touch the circle ABC in C , and from C let CA be drawn at ... touches the circle ABC , and FC is drawn from the assumed centre to the point of contact , Therefore FC is ...
Página 109
... touches the circle ABCD at the point B ( Hyp . ) , and BA is drawn at right angles to the tangent from the point of contact B ( Const . ) , The centre of the circle is in BA ( III . E 19 ) . F The centre is in BA . Therefore the angle ...
... touches the circle ABCD at the point B ( Hyp . ) , and BA is drawn at right angles to the tangent from the point of contact B ( Const . ) , The centre of the circle is in BA ( III . E 19 ) . F The centre is in BA . Therefore the angle ...
Página 110
... circle , containing an angle equal to the angleC . CASE I. - Let the angle C be a right IC A F H angle . CONSTRUCTION . - Bisect AB in F ( I. 10 ) . From the centre F , at ... touches the circle , PROOF . - Because from the 110 GEOMETRY .
... circle , containing an angle equal to the angleC . CASE I. - Let the angle C be a right IC A F H angle . CONSTRUCTION . - Bisect AB in F ( I. 10 ) . From the centre F , at ... touches the circle , PROOF . - Because from the 110 GEOMETRY .
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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.