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 Seiten |
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Seite 1
... Magnitudes may be considered under three dimensions , -length , breadth , height or thickness . 2. In Geometry there are several general terms or principles ; such as , Definitions , Propositions , Axioms , Theorems , Problems , Lemmas ...
... Magnitudes may be considered under three dimensions , -length , breadth , height or thickness . 2. In Geometry there are several general terms or principles ; such as , Definitions , Propositions , Axioms , Theorems , Problems , Lemmas ...
Seite 8
... magnitudes , lines , surfaces , or solids , are equal , if , when applied to each other , they coincide throughout their whole extent . They then fill the same space . 9. The whole is greater than any of its parts . 10. The whole is ...
... magnitudes , lines , surfaces , or solids , are equal , if , when applied to each other , they coincide throughout their whole extent . They then fill the same space . 9. The whole is greater than any of its parts . 10. The whole is ...
Seite 100
... magnitude of any kind , it signifies that the ... " magnitude is multiplied by the number . Thus , 3A signifies three " times A ; mB , m times B , or a multiple of B by m . When the num- " ber is intended to multiply two or more magnitudes ...
... magnitude of any kind , it signifies that the ... " magnitude is multiplied by the number . Thus , 3A signifies three " times A ; mB , m times B , or a multiple of B by m . When the num- " ber is intended to multiply two or more magnitudes ...
Seite 101
... Magnitudes are said to be of the same kind , when the less can be mul- tiplied so as to exceed the greater ; and it is only such magnitudes that are said to have a ratio to one another . 5. If there be four magnitudes , and if any ...
... Magnitudes are said to be of the same kind , when the less can be mul- tiplied so as to exceed the greater ; and it is only such magnitudes that are said to have a ratio to one another . 5. If there be four magnitudes , and if any ...
Seite 102
... magnitudes are continual proportionals , the ratio of the first to the third is said to be duplicate of the ratio of the first to the second " Thus , if A be to B as B to C , the ratio of A to C is said to be duplicate " of the ratio of ...
... magnitudes are continual proportionals , the ratio of the first to the third is said to be duplicate of the ratio of the first to the second " Thus , if A be to B as B to C , the ratio of A to C is said to be duplicate " of the ratio of ...
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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
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Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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...
Seite 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.
Seite 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...
Seite 134 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.