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, 1835 - 316 σελίδες |
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Αποτελέσματα 1 - 5 από τα 63.
Σελίδα
... whole work , not contained in any previous edition . A few useful Problems , especially in Surveying , are also added to the Sixth Book ; so that this edition of PLAYFAIR'S Geometry , it is presumed , will be found better adapted for ...
... whole work , not contained in any previous edition . A few useful Problems , especially in Surveying , are also added to the Sixth Book ; so that this edition of PLAYFAIR'S Geometry , it is presumed , will be found better adapted for ...
Σελίδα
... whole is so clearly and directly per- ceived , that I am persuaded no more difficulty will be found in understand- ing the propositions of the fifth Book than those of any other of the Ele- ments . In the second Book , also , some ...
... whole is so clearly and directly per- ceived , that I am persuaded no more difficulty will be found in understand- ing the propositions of the fifth Book than those of any other of the Ele- ments . In the second Book , also , some ...
Σελίδα 1
... whole of any thing is greater than a part of it ; or , the whole is equal to all its parts taken together ; or , two quantities that are each of them equal to a third quantity , are equal to each other . 5. A Theorem is a demonstrative ...
... whole of any thing is greater than a part of it ; or , the whole is equal to all its parts taken together ; or , two quantities that are each of them equal to a third quantity , are equal to each other . 5. A Theorem is a demonstrative ...
Σελίδα 8
... whole extent . They then fill the same space . 9. The whole is greater than any of its parts . 10. The whole is equal to the sum of all its parts . 11. All right angles are equal to one another . 12. " Two straight lines which intersect ...
... whole extent . They then fill the same space . 9. The whole is greater than any of its parts . 10. The whole is equal to the sum of all its parts . 11. All right angles are equal to one another . 12. " Two straight lines which intersect ...
Σελίδα 9
... whole triangle ABC shall coincide with the whole triangle DEF , so that the spaces which they contain or their areas are equal ; and the remaining angles of the one shall coincide with the remaining angles of the other , and be equal to ...
... whole triangle ABC shall coincide with the whole triangle DEF , so that the spaces which they contain or their areas are equal ; and the remaining angles of the one shall coincide with the remaining angles of the other , and be equal to ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angles equal arc AC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated diameter divided draw Prob equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular plane polygon prism PROP proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle 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 46 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Σελίδα 39 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Σελίδα 47 - 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 on the line between the points of section, is equal to the square on half the line.
Σελίδα 25 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel. Let AB, CD be equal and parallel straight lines, and joined towards the same parts by the straight lines AC, BD ; AC, BD are also equal and parallel.
Σελίδα 5 - 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 75 - 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.
Σελίδα 95 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
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 52 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle, having the obtuse angle...
Σελίδα 134 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.