Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with Explanatory Notes .... the first six booksJ. W. Parker & son, 1860 - 361 Seiten |
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Seite 14
... segment . If it be possible , let the segment AB be common to the two straight lines ABC , ABD . E D C A B From the point B , draw BE at right angles to 4B ; ( 1. 11. ) then because ABC is a straight line , therefore the angle ABE is ...
... segment . If it be possible , let the segment AB be common to the two straight lines ABC , ABD . E D C A B From the point B , draw BE at right angles to 4B ; ( 1. 11. ) then because ABC is a straight line , therefore the angle ABE is ...
Seite 43
... segment , " as Simson shews in his Corollary to Prop . 11 , Book 1 . 66 The following definition of straight lines has also been proposed . Straight lines are those which , if they coincide in any two points , coin- cide as far as they ...
... segment , " as Simson shews in his Corollary to Prop . 11 , Book 1 . 66 The following definition of straight lines has also been proposed . Straight lines are those which , if they coincide in any two points , coin- cide as far as they ...
Seite 44
... segment of a circle is not once alluded to in Book 1 , and is not required before the dis- cussion of the properties of the circle in Book III . Proclus remarks on this definition : " Hence you may collect that the center has three ...
... segment of a circle is not once alluded to in Book 1 , and is not required before the dis- cussion of the properties of the circle in Book III . Proclus remarks on this definition : " Hence you may collect that the center has three ...
Seite 61
... segment . " Has this corollary been tacitly assumed in any preceding proposition ? 45. In Euc . I. 12 , must the given line necessarily be " of unlimited length " ? 46. Shew that ( fig . Euc . 1. 11 ) every point without the perpendi ...
... segment . " Has this corollary been tacitly assumed in any preceding proposition ? 45. In Euc . I. 12 , must the given line necessarily be " of unlimited length " ? 46. Shew that ( fig . Euc . 1. 11 ) every point without the perpendi ...
Seite 76
... segments of the base made by the perpendicular from the vertex , according as the Engle is greater or less than a right angle . 37. If two exterior angles of a triangle be bisected , and from the point of intersection of the bisecting ...
... segments of the base made by the perpendicular from the vertex , according as the Engle is greater or less than a right angle . 37. If two exterior angles of a triangle be bisected , and from the point of intersection of the bisecting ...
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Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 54 - If two triangles have two sides of the one equal to two sides of the...
Seite 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...
Seite 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.
Seite 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.
Seite 18 - Any two angles of a triangle are together less than two right angles.
Seite 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.
Seite 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.
Seite 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.
Seite 3 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Seite 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...