Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with Explanatory Notes .... the first six booksJ. W. Parker & son, 1860 - 361 sider |
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Resultat 1-5 av 72
Side 22
... respectively equal to the three , A , B , C : and therefore the triangle KFG has its three sides KF , FG , GK , equal to the three given straight lines A , B , C. Q.E.F. PROPOSITION XXIII . PROBLEM . At a given point in a given straight ...
... respectively equal to the three , A , B , C : and therefore the triangle KFG has its three sides KF , FG , GK , equal to the three given straight lines A , B , C. Q.E.F. PROPOSITION XXIII . PROBLEM . At a given point in a given straight ...
Side 52
... respectively equal , the three angles of each shall be respectively equal . " But the converse is not universally true ; namely , If two triangles have the three angles in each respectively equal , the three sides are respectively equal ...
... respectively equal , the three angles of each shall be respectively equal . " But the converse is not universally true ; namely , If two triangles have the three angles in each respectively equal , the three sides are respectively equal ...
Side 57
... respectively equal to two sides of the other , and the contained angles supplemental , the two triangles are equal . A distinction ought to be made between equal triangles and equivalent triangles , the former including those whose ...
... respectively equal to two sides of the other , and the contained angles supplemental , the two triangles are equal . A distinction ought to be made between equal triangles and equivalent triangles , the former including those whose ...
Side 58
... respectively . If through the points of division of two contiguous sides of each of the squares upon the sides , lines be drawn parallel to the sides ( see the notes on Book II . ) , it will be ob- vious , that the squares will be ...
... respectively . If through the points of division of two contiguous sides of each of the squares upon the sides , lines be drawn parallel to the sides ( see the notes on Book II . ) , it will be ob- vious , that the squares will be ...
Side 61
... respectively equal to three elements of the other , the triangles are equal in every respect . " Enu- merate all the cases in which this equality is proved in the First Book . What case is omitted ? 57. What parts of a triangle must be ...
... respectively equal to three elements of the other , the triangles are equal in every respect . " Enu- merate all the cases in which this equality is proved in the First Book . What case is omitted ? 57. What parts of a triangle must be ...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ... Robert Potts Uten tilgangsbegrensning - 1845 |
Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson with ... Euclid,Robert Potts Uten tilgangsbegrensning - 1847 |
Vanlige uttrykk og setninger
A₁ ABCD AC is equal Algebraically angle ABC angle ACB angle BAC Apply Euc axiom base BC chord circle ABC constr describe a circle diagonals diameter divided double draw equal angles equiangular equilateral triangle equimultiples Euclid Euclid's Elements exterior angle Geometrical given circle given line given point given straight line given triangle gnomon greater hypotenuse inscribed intersection isosceles triangle less Let ABC line AC lines be drawn meet the circumference multiple opposite angles parallelogram pentagon perpendicular porism problem produced Prop proportionals proved Q.E.D. PROPOSITION quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angles right-angled triangle segment semicircle shew shewn similar similar triangles square on AC tangent THEOREM touch the circle trapezium triangle ABC twice the rectangle vertex vertical angle wherefore
Populære avsnitt
Side 54 - If two triangles have two sides of the one equal to two sides of the...
Side 89 - 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...
Side 38 - Let ABCD be the given rectilineal figure, and E the given rectilineal angle. It is required to describe a parallelogram equal to ABCD, and having an angle equal to E.
Side 144 - 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.
Side 18 - Any two angles of a triangle are together less than two right angles.
Side 266 - 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.
Side 152 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Side 7 - 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.
Side 3 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Side 96 - 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...