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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Αποτελέσματα 1 - 5 από τα 18.
Σελίδα 6
... straight lines being continually produced , shall at length meet upon that side on which are the angles which are less than two right angles . PROPOSITIONS . PROP . I. PROBLEM . To describe an equilateral triangle upon a given finite ...
... straight lines being continually produced , shall at length meet upon that side on which are the angles which are less than two right angles . PROPOSITIONS . PROP . I. PROBLEM . To describe an equilateral triangle upon a given finite ...
Σελίδα 7
... straight line , from a given point in the same . COR . By help of this problem , it may be demonstrated , that two straight lines cannot have a common segment . PROP . XII . PROBLEM . To draw a straight line perpendicular to a given ...
... straight line , from a given point in the same . COR . By help of this problem , it may be demonstrated , that two straight lines cannot have a common segment . PROP . XII . PROBLEM . To draw a straight line perpendicular to a given ...
Σελίδα 8
... straight lines cut one an- other , the angles which they make at the point where they cut , are together equal to ... given straight lines , but any two whatever of these must be greater than the third . PROP . XXIII . PROBLEM . At a given ...
... straight lines cut one an- other , the angles which they make at the point where they cut , are together equal to ... given straight lines , but any two whatever of these must be greater than the third . PROP . XXIII . PROBLEM . At a given ...
Σελίδα 9
... straight line falling upon two other straight lines make the alternate angles equal to one another ; these two ... given point parallel to a given straight line . PROP . XXXII . THEOREM . If a side of any triangle be produced , the ...
... straight line falling upon two other straight lines make the alternate angles equal to one another ; these two ... given point parallel to a given straight line . PROP . XXXII . THEOREM . If a side of any triangle be produced , the ...
Σελίδα 10
... straight line , and towards the same parts , are between the same parallels . PROP . XLI . THEOREM . If a ... given triangle , and have one of its angles equal to a given rectilineal angle . of PROP . XLIII . THEOREM . The complements of ...
... straight line , and towards the same parts , are between the same parallels . PROP . XLI . THEOREM . If a ... given triangle , and have one of its angles equal to a given rectilineal angle . of PROP . XLIII . THEOREM . The complements of ...
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...