The Elements of Euclid for the Use of Schools and Colleges: Comprising the First Six Books and Portions of the Eleventh and Twelfth BooksMacmillan, 1886 - 400 Seiten |
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Seite 3
... drawn from a certain point within the figure to the circumference are equal to one another : 16. And this point is called the centre of the circle . 17. A diameter of a circle is a straight line drawn through the centre , and terminated ...
... drawn from a certain point within the figure to the circumference are equal to one another : 16. And this point is called the centre of the circle . 17. A diameter of a circle is a straight line drawn through the centre , and terminated ...
Seite 8
... draw a straight line equal to a given straight line . Let A be the given point , and BC the given straight line : it ... drawn equal to the given straight line BC . Q.E.F. PROPOSITION 3. PROBLEM . From the greater of two given straight ...
... draw a straight line equal to a given straight line . Let A be the given point , and BC the given straight line : it ... drawn equal to the given straight line BC . Q.E.F. PROPOSITION 3. PROBLEM . From the greater of two given straight ...
Seite 16
... draw from the point Ca straight line at right angles to AB . A D C E B Take any point D in AC , and make CE equal to CD . [ I. 3 , On DE describe the equilateral triangle DFE , and join CF. [ I. 1 . The straight line CF drawn from the ...
... draw from the point Ca straight line at right angles to AB . A D C E B Take any point D in AC , and make CE equal to CD . [ I. 3 , On DE describe the equilateral triangle DFE , and join CF. [ I. 1 . The straight line CF drawn from the ...
Seite 17
... drawn from the given point C shall be perpendicular to the given straight line AB . Join CF , CG . Because FH is equal to HG , [ Construction . and HC is common to the two triangles FHC , GHC ; the two sides FH , HC are equal to the two ...
... drawn from the given point C shall be perpendicular to the given straight line AB . Join CF , CG . Because FH is equal to HG , [ Construction . and HC is common to the two triangles FHC , GHC ; the two sides FH , HC are equal to the two ...
Seite 67
... drawn from either of the acute angles to the opposite side pro- duced , the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle , by twice the rectangle contained by the ...
... drawn from either of the acute angles to the opposite side pro- duced , the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle , by twice the rectangle contained by the ...
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Häufige Begriffe und Wortgruppen
ABCD angle ABC angle ACB angle BAC angle EDF angles equal Axiom base BC BC is equal bisects the angle centre chord circle ABC circle described circumference Construction Corollary describe a circle diameter double draw a straight equal angles equal to F equiangular equilateral equimultiples Euclid Euclid's Elements exterior angle given circle given point given straight line gnomon Hypothesis inscribed intersect isosceles triangle less Let ABC magnitudes middle point multiple opposite angles opposite sides parallelogram perpendicular plane polygon produced proportionals PROPOSITION 13 Q.E.D. PROPOSITION quadrilateral radius rectangle contained rectilineal figure remaining angle rhombus right angles right-angled triangle segment shew shewn side BC square on AC straight line &c straight line drawn tangent THEOREM touches the circle triangle ABC triangle DEF twice the rectangle vertex Wherefore