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 2
... called a perpendicular to it . 11. An obtuse angle is that which is greater than a right angle . 12. An acute angle is that which is less than a right angle . 13. A term or boundary is the extremity of any 2 EUCLID'S ELEMENTS .
... called a perpendicular to it . 11. An obtuse angle is that which is greater than a right angle . 12. An acute angle is that which is less than a right angle . 13. A term or boundary is the extremity of any 2 EUCLID'S ELEMENTS .
Σελίδα 6
... 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 . PROPOSITION 1. PROBLEM . To describe an equilateral ...
... 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 . PROPOSITION 1. PROBLEM . To describe an equilateral ...
Σελίδα 9
... less . From the point A draw the straight line AD equal to C ; [ I. 2 . and from the centre A , at the distance AD , describe the circle DEF meeting AB at E. [ Postulate 3 . AE shall be equal to C. A B Because the point A is the centre ...
... less . From the point A draw the straight line AD equal to C ; [ I. 2 . and from the centre A , at the distance AD , describe the circle DEF meeting AB at E. [ Postulate 3 . AE shall be equal to C. A B Because the point A is the centre ...
Σελίδα 12
... less , and join DC . Then , because in the triangles DBC , ACB , DB is equal to AC , and BC is common to both , B [ I. 3 . [ Construction . the two sides DB , BC are equal to the two sides AC , CB , each to each ; and the angle DBC is ...
... less , and join DC . Then , because in the triangles DBC , ACB , DB is equal to AC , and BC is common to both , B [ I. 3 . [ Construction . the two sides DB , BC are equal to the two sides AC , CB , each to each ; and the angle DBC is ...
Σελίδα 19
... less to the greater ; which is impossible . Therefore BE is not in the same straight line with CB . And in the same manner it may be shewn that no other can be in the same straight line with it but BD ; therefore BD is in the same ...
... less to the greater ; which is impossible . Therefore BE is not in the same straight line with CB . And in the same manner it may be shewn that no other can be in the same straight line with it but BD ; therefore BD is in the same ...
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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.