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 3
... standing on another straight line , makes the adjacent angles equal to each other , each of these angles is called a right angle ; and the straight line which stands on the other is called a perpen- dicular to it . XI . An obtuse angle ...
... standing on another straight line , makes the adjacent angles equal to each other , each of these angles is called a right angle ; and the straight line which stands on the other is called a perpen- dicular to it . XI . An obtuse angle ...
Página 13
... stand upon the circumference intercepted between the straight lines that contain the angle . X. A sector of a circle , is the figure contained by two straight lines drawn from the centre , and the circumference between them . XI ...
... stand upon the circumference intercepted between the straight lines that contain the angle . X. A sector of a circle , is the figure contained by two straight lines drawn from the centre , and the circumference between them . XI ...
Página 16
... stand upon equal circumferences , whe- ther they be at the centres or circumferences . PROP . XXVII . THEOREM . In equal circles , the angles which stand upon equal circumferences , are equal to one another , whether they be at the ...
... stand upon equal circumferences , whe- ther they be at the centres or circumferences . PROP . XXVII . THEOREM . In equal circles , the angles which stand upon equal circumferences , are equal to one another , whether they be at the ...
Página 32
... stand have to one another : so also have the sectors . PROP . B. THEOREM . If an angle of a triangle be bisected by a straight line which likewise cuts the base ; the rectangle contained by the sides of the triangle is equal to the ...
... stand have to one another : so also have the sectors . PROP . B. THEOREM . If an angle of a triangle be bisected by a straight line which likewise cuts the base ; the rectangle contained by the sides of the triangle is equal to the ...
Página 35
... stand at right angles to each of two straight lines in the point of their intersection , it shall also be at right angles to the plane which passes through them , that is , to the plane in which they are . PROP . V. THEOREM . If three ...
... stand at right angles to each of two straight lines in the point of their intersection , it shall also be at right angles to the plane which passes through them , that is , to the plane in which they are . PROP . V. THEOREM . If three ...
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...