The definitions, postulates, axioms, and enunciations of the propositions of the first six, and the eleventh and twelfth books of Euclid's Elements of geometry1848 - 42 Seiten |
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Seite 16
... inscribed in a circle , are together equal to two right angles . PROP . XXIII . THEOREM . Upon the same straight line , and upon the same side of it , there cannot be two similar segments of circles , not coinciding with one another ...
... inscribed in a circle , are together equal to two right angles . PROP . XXIII . THEOREM . Upon the same straight line , and upon the same side of it , there cannot be two similar segments of circles , not coinciding with one another ...
Seite 18
... inscribed in another rectilineal figure , when all the angular points of the inscribed figure are upon the sides of the figure in which it is inscribed , each upon each . II . In like manner , a figure is said to be described about ...
... inscribed in another rectilineal figure , when all the angular points of the inscribed figure are upon the sides of the figure in which it is inscribed , each upon each . II . In like manner , a figure is said to be described about ...
Seite 19
... inscribe a square in a given circle . PROP . VII . PROBLEM . To describe a square about a given circle . PROP . VIII . PROBLEM . To inscribe a circle in a given square . PROP . IX . PROBLEM . To describe a circle about a given square ...
... inscribe a square in a given circle . PROP . VII . PROBLEM . To describe a square about a given circle . PROP . VIII . PROBLEM . To inscribe a circle in a given square . PROP . IX . PROBLEM . To describe a circle about a given square ...
Seite 40
... inscribed in circles , are to one another as the squares of their diameters . PROP . II . THEOREM . Circles are to one another as the squares of their diameters . PROP . III . THEOREM . Every pyramid having a triangular base , may be ...
... inscribed in circles , are to one another as the squares of their diameters . PROP . II . THEOREM . Circles are to one another as the squares of their diameters . PROP . III . THEOREM . Every pyramid having a triangular base , may be ...
Seite 42
... inscribe a polygon of an even number of equal sides , that shall not meet the less circle . LEMMA II . If two trapeziums ABCD , EFGH be inscribed in the circles , the centres of which are the points K , L ; and if the sides AB , DC be ...
... inscribe a polygon of an even number of equal sides , that shall not meet the less circle . LEMMA II . If two trapeziums ABCD , EFGH be inscribed in the circles , the centres of which are the points K , L ; and if the sides AB , DC be ...
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The Definitions, Postulates, Axioms, and Enunciations of the Propositions of ... Euclid Keine Leseprobe verfügbar - 2018 |
The Definitions, Postulates, Axioms, and Enunciations of the Propositions of ... Euclid Keine Leseprobe verfügbar - 2023 |
Häufige Begriffe und Wortgruppen
acute angle adjacent angles angle contained angles equal bases and altitudes bisect centre common section compounded of ratios cones and cylinders contained by three cuts the circle diameter equal circles equal straight lines equilateral and equiangular equilateral triangle equimultiples EUCLID'S ELEMENTS Ex æquali exterior angle four magnitudes four straight lines fourth given circle given rectilineal angle given rectilineal figure given straight line given triangle greater ratio homologous sides inscribed line be divided line be drawn lines be proportionals magnitude taken manifest multiple number of magnitudes obtuse angle parallel perpendicular polygons prisms PROBLEM PROP ratio compounded reciprocally proportional rectangle contained remaining ratio segment semicircle sides equal similar triangles similarly described solid angles solid figure contained solid parallelopiped solid polyhedron straight line drawn straight lines cut THEOREM third three plane angles three straight lines tiple triangular bases triangular pyramids Trinity College triplicate ratio unequal whole line XVIII XXIII
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Seite 8 - IF two triangles have two sides of the one equal to two sides of the...
Seite 29 - 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 6 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Seite 14 - From this it is manifest, that if in a circle a straight line bisect another at right angles, the centre of the circle is in the line which bisects the other.
Seite 23 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...
Seite 11 - 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.
Seite 13 - angle in a segment' is the angle contained by two straight lines drawn from any point in the circumference of the segment, to the extremities of the straight line which is the base of the segment.
Seite 12 - 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.
Seite 4 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Seite 30 - ABC, DEF have one angle in the one equal to one angle in the other, viz. the angle BAC to the angle EDF, and the sides about...