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 sider |
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Side 6
... triangle upon a given finite straight ... triangles have two sides of the one equal to two sides of the other , each to each ; and have likewise the angles contained by those sides equal to one another ; they shall likewise have their bases ...
... triangle upon a given finite straight ... triangles have two sides of the one equal to two sides of the other , each to each ; and have likewise the angles contained by those sides equal to one another ; they shall likewise have their bases ...
Side 7
... triangle are equal to one another : and if the equal sides be produced , the angles upon the other side of the base ... bases equal ; the angle which is contained by the two sides of the one shall be equal to the angle con- tained by ...
... triangle are equal to one another : and if the equal sides be produced , the angles upon the other side of the base ... bases equal ; the angle which is contained by the two sides of the one shall be equal to the angle con- tained by ...
Side 8
... triangle be produced , the exterior angle is greater than either of the interior opposite angles . PROP . XVII ... base of that which has the greater angle , shall be greater than the base of the other . PROP . XXV . THEOREM . If two ...
... triangle be produced , the exterior angle is greater than either of the interior opposite angles . PROP . XVII ... base of that which has the greater angle , shall be greater than the base of the other . PROP . XXV . THEOREM . If two ...
Side 9
... angle of the one to the third angle of the other . PROP . XXVII . THEOREM . If a straight line falling upon two other ... bases and between the same parallels , are equal to one another . PROP . XXXVII . THEOREM . Triangles upon the same ...
... angle of the one to the third angle of the other . PROP . XXVII . THEOREM . If a straight line falling upon two other ... bases and between the same parallels , are equal to one another . PROP . XXXVII . THEOREM . Triangles upon the same ...
Side 10
... Triangles upon equal bases and between the same parallels , are equal to one another . PROP . XXXIX . THEOREM . Equal triangles upon the same base and upon the same side of it , are between the same parallels . PROP . XL . THEOREM ...
... Triangles upon equal bases and between the same parallels , are equal to one another . PROP . XXXIX . THEOREM . Equal triangles upon the same base and upon the same side of it , are between the same parallels . PROP . XL . THEOREM ...
Andre utgaver - Vis alle
The Definitions, Postulates, Axioms and Enunciations of the Propositions of ... Uten tilgangsbegrensning - 1848 |
The Definitions, Postulates, Axioms, and Enunciations of the Propositions of ... Euclid Ingen forhåndsvisning tilgjengelig - 2018 |
The Definitions, Postulates, Axioms, and Enunciations of the Propositions of ... Euclid Ingen forhåndsvisning tilgjengelig - 2023 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 8 - IF two triangles have two sides of the one equal to two sides of the...
Side 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.
Side 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...
Side 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.
Side 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...
Side 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.
Side 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.
Side 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.
Side 4 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Side 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...