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 σελίδες |
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Σελίδα xv
... propositions . The propositions are of two kinds , pro- blems and theorems . In a problem something is required to be done ; in a theorem some new principle is asserted to be true . A proposition consists of various parts . We have ...
... propositions . The propositions are of two kinds , pro- blems and theorems . In a problem something is required to be done ; in a theorem some new principle is asserted to be true . A proposition consists of various parts . We have ...
Σελίδα xvi
... proposition itself . The word hypothesis is used in the same sense as supposition . To assist the student in following the steps of the reasoning , references are given to the results already ob- tained which are required in the ...
... proposition itself . The word hypothesis is used in the same sense as supposition . To assist the student in following the steps of the reasoning , references are given to the results already ob- tained which are required in the ...
Σελίδα 7
... PROPOSITION 1. PROBLEM . To describe an equilateral triangle on a given finite straight line . Let AB be the given straight line : it is required to describe an equilateral triangle on AB . D A Ε From the centre A , at the distance AB ...
... PROPOSITION 1. PROBLEM . To describe an equilateral triangle on a given finite straight line . Let AB be the given straight line : it is required to describe an equilateral triangle on AB . D A Ε From the centre A , at the distance AB ...
Σελίδα 8
... PROPOSITION 2. PROBLEM . From a given point to draw a straight line equal to a given straight line . Let A be the given point , and BC the given straight line : it is required to draw from the point A a straight line equal to BC . From ...
... PROPOSITION 2. PROBLEM . From a given point to draw a straight line equal to a given straight line . Let A be the given point , and BC the given straight line : it is required to draw from the point A a straight line equal to BC . From ...
Σελίδα 12
... PROPOSITION 6. THEOREM . If two angles of a triangle be equal to one another , the 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 ...
... PROPOSITION 6. THEOREM . If two angles of a triangle be equal to one another , the 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 ...
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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 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 35 - 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 equal to two right angles.
Σελίδα 67 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle, is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse angle, Let ABC be an obtuse-angled triangle, having the obtuse angle...
Σελίδα 73 - 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 284 - 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 50 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Σελίδα 57 - If a straight line be divided into two equal parts, and also into two unequal parts ; the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Σελίδα 10 - 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 227 - If two straight lines be at right angles to the same plane, they shall be parallel to one another. Let the straight lines AB, CD be at right angles to the same plane : AB is parallel to CD.
Σελίδα 102 - 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.
Σελίδα 352 - 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.