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 4
... sides equal : 26 . A scalene triangle is that which has three unequal sides : 27. A right - angled triangle is that which has a right angle : [ The side opposite to the right angle in a right - angled triangle is fre- quently called the ...
... sides equal : 26 . A scalene triangle is that which has three unequal sides : 27. A right - angled triangle is that which has a right angle : [ The side opposite to the right angle in a right - angled triangle is fre- quently called the ...
Seite 5
... sides equal to one another , but all its sides are not equal , nor its angles right angles : را 34. All other four - sided figures besides these are called trapeziums . 35. Parallel straight lines are such as are in the same plane , and ...
... sides equal to one another , but all its sides are not equal , nor its angles right angles : را 34. All other four - sided figures besides these are called trapeziums . 35. Parallel straight lines are such as are in the same plane , and ...
Seite 9
... sides of the one equal to two sides of the other , each to each , and have also the angles contained by those sides equal to one another , they shall also have their bases or third sides equal ; and the two triangles shall be equal ...
... sides of the one equal to two sides of the other , each to each , and have also the angles contained by those sides equal to one another , they shall also have their bases or third sides equal ; and the two triangles shall be equal ...
Seite 11
... sides FA , AC are equal to the two sides GA , AB , each to each ; and they contain the angle FAG common to the two triangles AFC , AGB ; therefore the base FC is equal to the base GB , and the triangle AFC to the triangle AGB , and the ...
... sides FA , AC are equal to the two sides GA , AB , each to each ; and they contain the angle FAG common to the two triangles AFC , AGB ; therefore the base FC is equal to the base GB , and the triangle AFC to the triangle AGB , and the ...
Seite 12
... sides also which subtend , or are oppo- site to , the equal angles , shall be equal to one another . Let ABC be a triangle , having the angle ABC equal to the angle ACB : the side AC shall be equal to the side AB . For if AC be not ...
... sides also which subtend , or are oppo- site to , the equal angles , shall be equal to one another . Let ABC be a triangle , having the angle ABC equal to the angle ACB : the side AC shall be equal to the side AB . For if AC be not ...
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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