The Elements of Euclid for the Use of Schools and CollegesMacmillan, 1872 - 400 Seiten |
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Seite 247
... formed by drawing straight lines to touch the circle at the points E , F , G , H ; and the square thus formed is greater than the circle ; therefore the square EFGH is greater than half of the circle . Bisect the arcs EF , FG , GH , HE ...
... formed by drawing straight lines to touch the circle at the points E , F , G , H ; and the square thus formed is greater than the circle ; therefore the square EFGH is greater than half of the circle . Bisect the arcs EF , FG , GH , HE ...
Seite 255
... formed by the base of a triangle and the sides pro- duced be equal , the sides of the triangle are equal ; this pro- position is true and will serve as an exercise for the student . The converse of a true proposition is not necessarily ...
... formed by the base of a triangle and the sides pro- duced be equal , the sides of the triangle are equal ; this pro- position is true and will serve as an exercise for the student . The converse of a true proposition is not necessarily ...
Seite 257
... formed on the other side of BC by these produced parts , and each of them would be equal to the angle BCG . The opinion has been maintained that even in I. I , it is tacitly assumed that the straight lines AC and BC cannot have a common ...
... formed on the other side of BC by these produced parts , and each of them would be equal to the angle BCG . The opinion has been maintained that even in I. I , it is tacitly assumed that the straight lines AC and BC cannot have a common ...
Seite 289
... formed , and if the vertices be put on the same side of the base another solid is formed . The two solids thus formed are con- tained by the same number of similar and equal plane figures , but they are not equal . It will be observed ...
... formed , and if the vertices be put on the same side of the base another solid is formed . The two solids thus formed are con- tained by the same number of similar and equal plane figures , but they are not equal . It will be observed ...
Seite 312
... formed , and the straight line which bisects the vertical angle of the triangle , meet at the same point . This may be shewn like 26 : if we adopt the second method we shall have to use VI . A. E 28. The perpendiculars drawn from the ...
... formed , and the straight line which bisects the vertical angle of the triangle , meet at the same point . This may be shewn like 26 : if we adopt the second method we shall have to use VI . A. E 28. The perpendiculars drawn from the ...
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Häufige Begriffe und Wortgruppen
ABCD AC is equal angle ABC angle ACB angle BAC angle EDF angles equal Axiom base BC 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