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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... . The Aphorisms which form a prefix of 174 pages , may suggest useful reflections to earnest students . " - The Patriot . JOHN W. PARKER & SON , West Strand , London . EUCLID'S ELEMENTS OF GEOMETRY . BOOK I. DEFINITIONS . I.
... . The Aphorisms which form a prefix of 174 pages , may suggest useful reflections to earnest students . " - The Patriot . JOHN W. PARKER & SON , West Strand , London . EUCLID'S ELEMENTS OF GEOMETRY . BOOK I. DEFINITIONS . I.
Seite 3
... , or triangles , by three straight lines . XXII . Quadrilateral , by four straight lines . XXIII . Multilateral figures , or polygons , by more than four straight lines . XXIV . Of three - sided figures , an equilateral B 2 DEFINITIONS .
... , or triangles , by three straight lines . XXII . Quadrilateral , by four straight lines . XXIII . Multilateral figures , or polygons , by more than four straight lines . XXIV . Of three - sided figures , an equilateral B 2 DEFINITIONS .
Seite 5
... straight line may be produced to any length in a straight line . III . And that a circle may be described from any center , at any distance from that center . AXIOMS . I. THINGS which are equal to the same DEFINITIONS . 5 .
... straight line may be produced to any length in a straight line . III . And that a circle may be described from any center , at any distance from that center . AXIOMS . I. THINGS which are equal to the same DEFINITIONS . 5 .
Seite 41
... the angle BAC ; ( 1. 8. ) but DAC is a right angle ; therefore also BAC is a right angle . Therefore , if the square described upon , & c . Q. E. D. ON THE DEFINITIONS . GEOMETRY is one of the most BOOK 1. PROP . XLVIII . 41.
... the angle BAC ; ( 1. 8. ) but DAC is a right angle ; therefore also BAC is a right angle . Therefore , if the square described upon , & c . Q. E. D. ON THE DEFINITIONS . GEOMETRY is one of the most BOOK 1. PROP . XLVIII . 41.
Seite 42
... definitions of the latter . Def . I. Simson has adopted Theon's definition of a point . Euclid's definition is , σημεῖον ἐστιν οὗ μέρος οὐδέν , “ A point is that , of which there is no part , or which cannot be parted or divided , as it ...
... definitions of the latter . Def . I. Simson has adopted Theon's definition of a point . Euclid's definition is , σημεῖον ἐστιν οὗ μέρος οὐδέν , “ A point is that , of which there is no part , or which cannot be parted or divided , as it ...
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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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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...