The Elements of Euclid for the Use of Schools and CollegesMacmillan, 1872 - 400 sider |
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Side 1
... taken , the straight line between them lies wholly in that superficies . 8. A plane angle is the inclination of two lines to one another in a plane , which meet together , but are not in the same direction . 9. A plane rectilineal angle ...
... taken , the straight line between them lies wholly in that superficies . 8. A plane angle is the inclination of two lines to one another in a plane , which meet together , but are not in the same direction . 9. A plane rectilineal angle ...
Side 6
... taken from equals the remainders are equal . 4. If equals be added to unequals the wholes are unequal . 5. If equals be taken from unequals the remainders are unequal . 6. Things which are double of the same thing are equal to one ...
... taken from equals the remainders are equal . 4. If equals be added to unequals the wholes are unequal . 5. If equals be taken from unequals the remainders are unequal . 6. Things which are double of the same thing are equal to one ...
Side 33
... taken together , less than two right angles , these straight lines being continually produced , shall at length meet on that side on which are the angles which are less than two right angles . [ Axiom 12 . Therefore the straight lines ...
... taken together , less than two right angles , these straight lines being continually produced , shall at length meet on that side on which are the angles which are less than two right angles . [ Axiom 12 . Therefore the straight lines ...
Side 73
... this it is manifest , that if in a circle a straight line bisect another at right angles , the centre of the circle is in the straight line which bisects the other . PROPOSITION 2. THEOREM . If any two points be taken BOOK III . 1 . 73.
... this it is manifest , that if in a circle a straight line bisect another at right angles , the centre of the circle is in the straight line which bisects the other . PROPOSITION 2. THEOREM . If any two points be taken BOOK III . 1 . 73.
Side 74
Isaac Todhunter. PROPOSITION 2. THEOREM . If any two points be taken in the circumference of a circle , the straight line which joins them shall fall within the circle . Let ABC be a circle , and A and B any two points in the ...
Isaac Todhunter. PROPOSITION 2. THEOREM . If any two points be taken in the circumference of a circle , the straight line which joins them shall fall within the circle . Let ABC be a circle , and A and B any two points in the ...
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Vanlige uttrykk og setninger
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