Euclid Revised: Containing the Essentials of the Elements of Plane Geometry as Given by Euclid in His First Six Books, with Numerous Additional Propositions and ExercisesClarendon Press, 1890 - 400 σελίδες |
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Αποτελέσματα 1 - 5 από τα 79.
Σελίδα 10
... sides and the included angle of the other , then the triangles are iden- tically equal , and of the angles those are equal which are opposite equal sides . A D ДД B E Let ABC , DEF be two As , in which and AB = DE , AC = DF , BẬC = EDE ...
... sides and the included angle of the other , then the triangles are iden- tically equal , and of the angles those are equal which are opposite equal sides . A D ДД B E Let ABC , DEF be two As , in which and AB = DE , AC = DF , BẬC = EDE ...
Σελίδα 11
... sides of a triangle are equal , the angles which are opposite to them are equal . B C ' Let ABC be a △ , in which ... sides equal it is called isosceles ; the third side is called the base ; the angle opposite the base is called the ...
... sides of a triangle are equal , the angles which are opposite to them are equal . B C ' Let ABC be a △ , in which ... sides equal it is called isosceles ; the third side is called the base ; the angle opposite the base is called the ...
Σελίδα 13
... sides of the other , then the triangles are identically equal , and of the angles those are equal which are opposite equal sides . 444 Let the As be placed so that- 1o , a pair of equal sides may have a coincident position BC : 2o , the ...
... sides of the other , then the triangles are identically equal , and of the angles those are equal which are opposite equal sides . 444 Let the As be placed so that- 1o , a pair of equal sides may have a coincident position BC : 2o , the ...
Σελίδα 18
... opposite sides of it , make the adjacent angles together equal to two right angles , these two straight lines must be in one and the same straight line . B Z X A Y At the point A in the st . line AB , let the st . lines AX , AY , on ...
... opposite sides of it , make the adjacent angles together equal to two right angles , these two straight lines must be in one and the same straight line . B Z X A Y At the point A in the st . line AB , let the st . lines AX , AY , on ...
Σελίδα 19
... side of this equality , we have BAZ = BÂY = BÂY , which cannot be , unless AZ lie along AY . .. XA , AY are in a st . line . Proposition 15 . THEOREM - If two straight lines cut one another , the ver- tically opposite angles are equal ...
... side of this equality , we have BAZ = BÂY = BÂY , which cannot be , unless AZ lie along AY . .. XA , AY are in a st . line . Proposition 15 . THEOREM - If two straight lines cut one another , the ver- tically opposite angles are equal ...
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD Addenda altitude base bisector bisects centre of similitude chord circum-circle circumf circumference coincide collinear concyclic corners cross-ratio cyclic quadrilateral diag diagonals diam diameter divided draw drawn equal angles equiang Euclid find the Locus fixed circle fixed line fixed point given circle given line given point harmonic conjugates inscribed intersection inverse Join Let ABC magnitudes meet mid point mid pt Note-The NOTE-Use opposite sides pair parallel parallelogram pedal triangle perpendicular polygon PROBLEM-To produced Prop Proposition Proposition 13 Ptolemy's Theorem quad radical axis radii radius ratio rect rectangle rectilineal figure respectively right angles segments segt Similarly simr Simson's Line square straight line tang tangents THEOREM THEOREM-If touch triangle ABC variable
Δημοφιλή αποσπάσματα
Σελίδα 251 - 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 29 - 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 150 - If a straight line touch a circle, and from the point of contact a chord be drawn, the angles which this chord makes with the tangent are equal to the angles in the alternate segments.
Σελίδα 91 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square on the other part.
Σελίδα 82 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Σελίδα 37 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.
Σελίδα 44 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Σελίδα 84 - Iff 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 22 - Any two sides of a triangle are together greater than the third side.
Σελίδα 87 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square...