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 29
... sides , be divided into two equal angles , by a straight line which also cuts the base produced ; the segments ... homologous sides . PROP . VI . THEOREM . If two triangles have one angle of the one equal to one angle of the other , and ...
... sides , be divided into two equal angles , by a straight line which also cuts the base produced ; the segments ... homologous sides . PROP . VI . THEOREM . If two triangles have one angle of the one equal to one angle of the other , and ...
Side 30
... sides about the equal angles reciprocally pro- portional : and conversely , parallelograms that have one angle of ... homologous sides . COR . From this it is manifest , that if three straight lines be propor- tionals , as the first is ...
... sides about the equal angles reciprocally pro- portional : and conversely , parallelograms that have one angle of ... homologous sides . COR . From this it is manifest , that if three straight lines be propor- tionals , as the first is ...
Side 38
... homologous sides . COR . From this it is manifest , that , if four straight lines be continual proportionals , as the first is to the fourth , so is the solid parallelopiped described from the first to the similar solid similarly ...
... homologous sides . COR . From this it is manifest , that , if four straight lines be continual proportionals , as the first is to the fourth , so is the solid parallelopiped described from the first to the similar solid similarly ...
Side 41
... homologous sides . COR . From this it is evident , that similar pyramids which have multangular bases , are likewise to one another in the triplicate ratio of their homologous sides : for they may be divided into similar pyramids having ...
... homologous sides . COR . From this it is evident , that similar pyramids which have multangular bases , are likewise to one another in the triplicate ratio of their homologous sides : for they may be divided into similar pyramids having ...
Side 42
... sides , that shall not meet the less circle . LEMMA II . If two trapeziums ABCD , EFGH be inscribed in the circles ... homologous sides . Therefore the pyra- mid of which the base is the quadrilateral KBOS , and vertex A , has to the ...
... sides , that shall not meet the less circle . LEMMA II . If two trapeziums ABCD , EFGH be inscribed in the circles ... homologous sides . Therefore the pyra- mid of which the base is the quadrilateral KBOS , and vertex A , has to the ...
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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...