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 páginas |
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Página 11
... contained by any two of the straight lines which contain one of the right angles . II . In every parallelogram , any ... rectangle contained by the two straight lines , is equal to the rectangles contained by the undivided line , and the ...
... contained by any two of the straight lines which contain one of the right angles . II . In every parallelogram , any ... rectangle contained by the two straight lines , is equal to the rectangles contained by the undivided line , and the ...
Página 12
... rectangle con- tained by the whole and that part , together with the square of the other part . PROP . VIII . THEOREM . If a straight line be divided into any two parts , four times the rectangle contained by the whole line , and one of ...
... rectangle con- tained by the whole and that part , together with the square of the other part . PROP . VIII . THEOREM . If a straight line be divided into any two parts , four times the rectangle contained by the whole line , and one of ...
Página 17
... contain an angle equal to a given rectilineal angle . PROP . XXXV . THEOREM . If two straight lines cut one another within a circle , the rectangle con- tained by the segments of one of them , is equal to the rectangle contained by the ...
... contain an angle equal to a given rectilineal angle . PROP . XXXV . THEOREM . If two straight lines cut one another within a circle , the rectangle con- tained by the segments of one of them , is equal to the rectangle contained by the ...
Página 30
... rectangle contained by the extremes is equal to the rectangle contained by the means : and con- versely , if the rectangle contained by the extremes be equal to the rectangle contained by the means , the four straight lines are ...
... rectangle contained by the extremes is equal to the rectangle contained by the means : and con- versely , if the rectangle contained by the extremes be equal to the rectangle contained by the means , the four straight lines are ...
Página 32
... rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base , together with the square of the straight line , which bisects the angle . PROP . C. THEOREM . If from any angle of a ...
... rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base , together with the square of the straight line , which bisects the angle . PROP . C. THEOREM . If from any angle of a ...
Otras ediciones - Ver todas
The Definitions, Postulates, Axioms and Enunciations of the Propositions of ... Vista completa - 1848 |
The Definitions, Postulates, Axioms, and Enunciations of the Propositions of ... Euclid Sin vista previa disponible - 2018 |
The Definitions, Postulates, Axioms, and Enunciations of the Propositions of ... Euclid Sin vista previa disponible - 2023 |
Términos y frases comunes
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
Pasajes populares
Página 8 - IF two triangles have two sides of the one equal to two sides of the...
Página 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.
Página 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...
Página 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.
Página 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...
Página 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.
Página 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.
Página 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.
Página 4 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Página 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...