The Elements of Euclid for the Use of Schools and Colleges: Comprising the First Six Books and Portions of the Eleventh and Twelfth Books : with Notes, an Appendix, and ExercisesMacmillan, 1867 - 400 páginas |
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Página 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 ...
Página 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 ...
Página 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 ...
Página 74
... 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 circumference : the straight line drawn from A to B shall fall within the ...
... 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 circumference : the straight line drawn from A to B shall fall within the ...
Página 77
... Axiom 1 . the less to the greater ; which is impossible . Therefore F is not the centre of the circles ABC , CDE . Wherefore , if two circles & c . Q.E.D. PROPOSITION 7. THEOREM . If any point be taken in BOOK III . 5 , 6 . 77.
... Axiom 1 . the less to the greater ; which is impossible . Therefore F is not the centre of the circles ABC , CDE . Wherefore , if two circles & c . Q.E.D. PROPOSITION 7. THEOREM . If any point be taken in BOOK III . 5 , 6 . 77.
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Términos y frases comunes
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
Pasajes populares
Página 286 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Página 30 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Página 34 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon the same side; and likewise the two interior angles upon the same side together equal to two right angles...
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 together equal to two right angles.
Página 12 - 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.
Página 302 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.
Página 220 - If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Página 354 - Prove that the square on any straight line drawn from the vertex of an isosceles triangle to the base, is less than the square on a side of the triangle by the rectangle contained by the segments of the base : and conversely.
Página 104 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Página 96 - The opposite angles of any quadrilateral figure inscribed in a circle, are together equal to two right angles.