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 σελίδες |
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Σελίδα 20
... ratio are called proportionals . ' N. B. When four magnitudes are proportionals , it is usually ex- pressed by saying , the first is to the second , as the third to the fourth . ' . VII . When of the equimultiples of four magnitudes ...
... ratio are called proportionals . ' N. B. When four magnitudes are proportionals , it is usually ex- pressed by saying , the first is to the second , as the third to the fourth . ' . VII . When of the equimultiples of four magnitudes ...
Σελίδα 21
... proportionals . Definition A , to wit , of compound ratio . When there are any number of magnitudes of the same kind , the first is said to have to the last of them the ratio compounded of the ratio which the first has to the second ...
... proportionals . Definition A , to wit , of compound ratio . When there are any number of magnitudes of the same kind , the first is said to have to the last of them the ratio compounded of the ratio which the first has to the second ...
Σελίδα 22
... proportionals , and it is inferred that the first together with the second , is to the second , as the third together with the fourth , is to the fourth . Prop . 18 , Book v . XVI . Dividendo , by division ; when there are four ...
... proportionals , and it is inferred that the first together with the second , is to the second , as the third together with the fourth , is to the fourth . Prop . 18 , Book v . XVI . Dividendo , by division ; when there are four ...
Σελίδα 24
... proportionals , they are proportionals also when taken inversely . PROP . C. THEOREM . If the first be the same multiple of the second , or the same part of it , that the third is of the fourth ; the first is to the second , as the ...
... proportionals , they are proportionals also when taken inversely . PROP . C. THEOREM . If the first be the same multiple of the second , or the same part of it , that the third is of the fourth ; the first is to the second , as the ...
Σελίδα 25
... proportionals , as one of the ante- cedents is to its consequent , so shall all the antecedents taken together be to ... proportionals , they shall also be proportionals when taken alternately . PROP . XVII . THEOREM . If magnitudes ...
... proportionals , as one of the ante- cedents is to its consequent , so shall all the antecedents taken together be to ... proportionals , they shall also be proportionals when taken alternately . PROP . XVII . THEOREM . If magnitudes ...
Άλλες εκδόσεις - Προβολή όλων
The Definitions, Postulates, Axioms and Enunciations of the Propositions of ... Πλήρης προβολή - 1848 |
The Definitions, Postulates, Axioms, and Enunciations of the Propositions of ... Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
The Definitions, Postulates, Axioms, and Enunciations of the Propositions of ... Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2023 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 8 - IF two triangles have two sides of the one equal to two sides of the...
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 4 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Σελίδα 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...