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 4
... straight lines drawn from a certain point within the figure to the circumference , are equal to one another . XVI ... four straight lines . XXIII . Multilateral figures , or polygons , by more than four straight lines . XXIV . Of three ...
... straight lines drawn from a certain point within the figure to the circumference , are equal to one another . XVI ... four straight lines . XXIII . Multilateral figures , or polygons , by more than four straight lines . XXIV . Of three ...
Side 5
... four - sided figures besides these , are called Trapeziums . XXXV . Parallel straight lines are such as are in the same plane , and which being produced ever so far both ways , do not meet . A. A parallelogram is a four - sided figure ...
... four - sided figures besides these , are called Trapeziums . XXXV . Parallel straight lines are such as are in the same plane , and which being produced ever so far both ways , do not meet . A. A parallelogram is a four - sided figure ...
Side 8
... straight lines cut one an- other , the angles which they make at the point where they cut , are together equal to four right angles . COR . 2. And consequently , that all the angles made by any number of lines meeting in one point , are ...
... straight lines cut one an- other , the angles which they make at the point where they cut , are together equal to four right angles . COR . 2. And consequently , that all the angles made by any number of lines meeting in one point , are ...
Side 9
... straight lines make the alternate angles equal to one another ; these two straight lines shall be parallel . PROP ... four right angles , are equal to twice as many right angles as the figure has sides . COR . 2. All the exterior angles of ...
... straight lines make the alternate angles equal to one another ; these two straight lines shall be parallel . PROP ... four right angles , are equal to twice as many right angles as the figure has sides . COR . 2. All the exterior angles of ...
Side 30
Euclides. PROP . XII . PROBLEM . To find a fourth proportional to three given straight lines . PROP . XIII . PROBLEM . To find a mean proportional between two given straight lines . PROP . XIV . THEOREM . Equal parallelograms , which ...
Euclides. PROP . XII . PROBLEM . To find a fourth proportional to three given straight lines . PROP . XIII . PROBLEM . To find a mean proportional between two given straight lines . PROP . XIV . THEOREM . Equal parallelograms , which ...
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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...