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, 1883 - 400 σελίδες |
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Σελίδα 14
... . [ Axiom 8 . Wherefore , if two triangles & c . Q.E.D. PROPOSITION 9. PROBLEM . To bisect a given rectilineal angle , that is to divide it into two equal angles . Let BAC be the given rectilineal angle : it is 14 EUCLID'S ELEMENTS .
... . [ Axiom 8 . Wherefore , if two triangles & c . Q.E.D. PROPOSITION 9. PROBLEM . To bisect a given rectilineal angle , that is to divide it into two equal angles . Let BAC be the given rectilineal angle : it is 14 EUCLID'S ELEMENTS .
Σελίδα 15
... bisect it . Take any point D in AB , and from AC cut off AE equal to AD ; [ I. 3 . join DE , and on DE , on the side ... bisected by the straight line AF . Q.E.F. PROPOSITION 10 . PROBLEM . To bisect a given finite straight line , that ...
... bisect it . Take any point D in AB , and from AC cut off AE equal to AD ; [ I. 3 . join DE , and on DE , on the side ... bisected by the straight line AF . Q.E.F. PROPOSITION 10 . PROBLEM . To bisect a given finite straight line , that ...
Σελίδα 17
... Bisect FG at H , and join CH . [ Postulate 3 . [ I. 10 . The straight line CH 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 ...
... Bisect FG at H , and join CH . [ Postulate 3 . [ I. 10 . The straight line CH 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 ...
Σελίδα 20
... Bisect AC at E , [ I. 10 . join BE and produce it to F , making EF equal to EB , [ I. 3 . and join FC . Because AE is equal to EC , and BE to EF ; [ Constr . the two sides AE , EB are equal to the two sides CE , EF , each to each ; and ...
... Bisect AC at E , [ I. 10 . join BE and produce it to F , making EF equal to EB , [ I. 3 . and join FC . Because AE is equal to EC , and BE to EF ; [ Constr . the two sides AE , EB are equal to the two sides CE , EF , each to each ; and ...
Σελίδα 21
... bisected , and the side AC be produced to G , it may be shewn that the angle BCG , that is the angle ACD , is greater than the angle ABC . [ I. 15 . Wherefore , if one side & c . Q.E.D. PROPOSITION 17. THEOREM . Any two angles of a ...
... bisected , and the side AC be produced to G , it may be shewn that the angle BCG , that is the angle ACD , is greater than the angle ABC . [ I. 15 . Wherefore , if one side & c . Q.E.D. PROPOSITION 17. THEOREM . Any two angles of a ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 262 - 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.
Σελίδα 71 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a Right Angle; and the straight line which stands on the other is called a Perpendicular to it.
Σελίδα 262 - To draw a straight line at right angles to a given straight line, from a given point in the same. Let AB be...
Σελίδα 182 - 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.
Σελίδα 8 - 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.
Σελίδα 298 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.
Σελίδα 58 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Σελίδα 60 - If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line, and of the square on the line between the points of section. Let the straight line AB be divided into two equal parts in the point C, and into two unequal parts in the point D ; The squares on AD and DB shall be together double of AD»+DB
Σελίδα 242 - Let AB and C be two unequal magnitudes, of which AB is the greater. If from AB there be taken more than its half, and from the remainder more than its half, and so on ; there shall at length remain a magnitude less than C. For C may be multiplied, so at length to become greater than AB.
Σελίδα 4 - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.