Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids : to which are Added Elements of Plane and Spherical TrigonometryW.E. Dean, 1853 - 317 σελίδες |
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Αποτελέσματα 1 - 5 από τα 87.
Σελίδα 4
... propositions of the fifth Book than those of any other of the Elements . In the second Book , also , some algebraic signs have been introduced , for the sake of representing more readily the addition and subtraction of the rectangles on ...
... propositions of the fifth Book than those of any other of the Elements . In the second Book , also , some algebraic signs have been introduced , for the sake of representing more readily the addition and subtraction of the rectangles on ...
Σελίδα 5
... proposition , requiring no forinal demonstration to prove the truth of it ; but is received and assented to as soon as mentioned . the Such as , the whole of any thing is greater than a part of it ; or , whole is equal to all its parts ...
... proposition , requiring no forinal demonstration to prove the truth of it ; but is received and assented to as soon as mentioned . the Such as , the whole of any thing is greater than a part of it ; or , whole is equal to all its parts ...
Σελίδα 6
... proposition to be true , by proving that some absurdity would necessarily follow if the proposition advanced were false . This is sometimes called Reductio ad Absurdum ; because it shows the absurdity and falsehood of all suppositions ...
... proposition to be true , by proving that some absurdity would necessarily follow if the proposition advanced were false . This is sometimes called Reductio ad Absurdum ; because it shows the absurdity and falsehood of all suppositions ...
Σελίδα 7
... proposition and the Book in which it has been announced or de- monstrated . The expression ( 15. 1. ) denotes the fifteenth proposition , first book , and so on . In like manner , ( 3. Ax . ) designates the third axiom ; ( 2. Post ...
... proposition and the Book in which it has been announced or de- monstrated . The expression ( 15. 1. ) denotes the fifteenth proposition , first book , and so on . In like manner , ( 3. Ax . ) designates the third axiom ; ( 2. Post ...
Σελίδα 11
... to one another . 11. " Two straight lines which intersect one another , cannot be both pa- " rallel to the same straight line . " PROPOSITION I. PROBLEM . To describe an equilateral triangle upon OF GEOMETRY . BOOK I. 11.
... to one another . 11. " Two straight lines which intersect one another , cannot be both pa- " rallel to the same straight line . " PROPOSITION I. PROBLEM . To describe an equilateral triangle upon OF GEOMETRY . BOOK I. 11.
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated described diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROB PROP proportional proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR touches the circle triangle ABC triangle DEF wherefore
Δημοφιλή αποσπάσματα
Σελίδα 51 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Σελίδα 74 - THE angles in the same segment of a circle are equal to one another...
Σελίδα 37 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Σελίδα 29 - Straight lines which are parallel to the same straight line are parallel to one another. Triangles and Rectilinear Figures. The sum of the angles of a triangle is equal to two right angles.
Σελίδα 29 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line through EAF the point A, parallel to the straight line '
Σελίδα 147 - If the vertical angle of a triangle be bisected by a straight line which also cute the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Σελίδα 19 - The angles which one straight line makes with another upon one side of i't, are either two right angles, or are together eqval to two right angles.
Σελίδα 134 - IF three straight lines be proportionals, the rectangle contained by the extremes is equal to the square of the mean : and if the rectangle contained by the extremes be equal to the square of the mean, the three straight lines are proportionals.
Σελίδα 294 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 13 - BC. Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC.