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 5
... described from any centre at any distance from that centre . AXIOMS . I. THINGS which are equal to the same thing are equal to one another . II . If equals be added to equals , the wholes are equal . III . If equals be taken from equals ...
... described from any centre at any distance from that centre . AXIOMS . I. THINGS which are equal to the same thing are equal to one another . II . If equals be added to equals , the wholes are equal . III . If equals be taken from equals ...
Seite 10
... described upon the side subtending the right angle , is equal to the squares described upon the sides which contain the right angle . PROP . XLVIII . THEOREM . If the square described upon one of the sides of a triangle , be equal to ...
... described upon the side subtending the right angle , is equal to the squares described upon the sides which contain the right angle . PROP . XLVIII . THEOREM . If the square described upon one of the sides of a triangle , be equal to ...
Seite 18
... described about another figure , when all the sides of the circumscribed figure pass through the angular points of the figure about which it is described , each through each . III . A rectilineal figure is said to be inscribed in a ...
... described about another figure , when all the sides of the circumscribed figure pass through the angular points of the figure about which it is described , each through each . III . A rectilineal figure is said to be inscribed in a ...
Seite 30
... described triangle upon the second . PROP . XX . THEOREM . Similar polygons may be divided into the same number of similar triangles , having the same ratio to one another that the polygons have ; and the polygons have to one another ...
... described triangle upon the second . PROP . XX . THEOREM . Similar polygons may be divided into the same number of similar triangles , having the same ratio to one another that the polygons have ; and the polygons have to one another ...
Seite 31
... described upon them shall also be proportionals : and conversely , if the similar rectilineal figures similarly described upon four straight lines be proportionals , those straight lines shall be proportionals . PROP . XXIII . THEOREM ...
... described upon them shall also be proportionals : and conversely , if the similar rectilineal figures similarly described upon four straight lines be proportionals , those straight lines shall be proportionals . PROP . XXIII . THEOREM ...
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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...