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, 1846 - 317 σελίδες |
Αναζήτηση στο βιβλίο
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 . Such as , the whole of any thing is greater than a part of it ; or , the 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 . Such as , the whole of any thing is greater than a part of it ; or , the 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 ...
... 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 ...
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 " rallel to the same straight line . " pa- 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 " rallel to the same straight line . " pa- PROPOSITION I. PROBLEM . To describe an equilateral triangle upon OF GEOMETRY . BOOK I. 11.
Άλλες εκδόσεις - Προβολή όλων
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 magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular plane 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 third touches the circle triangle ABC triangle DEF wherefore
Δημοφιλή αποσπάσματα
Σελίδα 49 - 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 147 - ... cuts 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 292 - 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 7 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Σελίδα 139 - K hag to M the ratio which is compounded of the ratios of the sides ; therefore also the parallelogram AC has to the parallelogram CF the ratio which is compounded of the ratios of the sides. COR. Hence, any two rectangles are to each other as the products of their bases multiplied by their altitudes.
Σελίδα 33 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Σελίδα 79 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles made by...
Σελίδα 125 - 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 131 - If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means; And if the rectangle contained by the extremes be equal to the rectangle contained by the means, the four straight lines are proportionals. Let the four straight lines, AB, CD, E, F, be proportionals, viz.
Σελίδα 78 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.