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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Resultater 1-5 af 48
Side 17
... vertical , or opposite angles shall be equal . Let the two straight lines AB , CD cut one another in the point E. Then the angle AEC shall be equal to the angle DEB , and the angle CEB to the angle AED . C A- E Because the straight line ...
... vertical , or opposite angles shall be equal . Let the two straight lines AB , CD cut one another in the point E. Then the angle AEC shall be equal to the angle DEB , and the angle CEB to the angle AED . C A- E Because the straight line ...
Side 18
... angle AEB is equal to the angle CEF , because they are opposite vertical angles ; ( I. 15. ) therefore the base AB is equal to the base CF , ( I. 4. ) and the triangle AEB to the triangle CEF , and the remaining angles of one triangle ...
... angle AEB is equal to the angle CEF , because they are opposite vertical angles ; ( I. 15. ) therefore the base AB is equal to the base CF , ( I. 4. ) and the triangle AEB to the triangle CEF , and the remaining angles of one triangle ...
Side 53
... angle EAF is equal to the angle EDF , ( ax . 2 or 3 ) : or the angle BDC is ... angles . If FA be produced in the fig . Prop . 9 , it bisects the angle which is the ... vertical angles made by four straight lines at the same point be ...
... angle EAF is equal to the angle EDF , ( ax . 2 or 3 ) : or the angle BDC is ... angles . If FA be produced in the fig . Prop . 9 , it bisects the angle which is the ... vertical angles made by four straight lines at the same point be ...
Side 62
... angle contained between the perpendiculars drawn to two given straight lines ... vertical angles , and alternate angles ; and give examples from the First ... angle . 72. Taking as the definition of parallel straight lines that they are ...
... angle contained between the perpendiculars drawn to two given straight lines ... vertical angles , and alternate angles ; and give examples from the First ... angle . 72. Taking as the definition of parallel straight lines that they are ...
Side 63
... vertical angles . 79. If two straight lines join the extremities of two parallel straight lines , but not towards the same parts , when are the joining lines equal , and when are they unequal ? 80. If either diameter of a four - sided ...
... vertical angles . 79. If two straight lines join the extremities of two parallel straight lines , but not towards the same parts , when are the joining lines equal , and when are they unequal ? 80. If either diameter of a four - sided ...
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Almindelige termer og sætninger
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
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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...