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 páginas |
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Página 7
... line may be produced to any length in a straight line . 3. And that a circle may be described from any centre , at any distance from that centre . AXIOMS . 1. THINGS which are equal to the same OF GEOMETRY . BOOK I. 7.
... line may be produced to any length in a straight line . 3. And that a circle may be described from any centre , at any distance from that centre . AXIOMS . 1. THINGS which are equal to the same OF GEOMETRY . BOOK I. 7.
Página 30
... described upon the side sub- tending the right angle , is equivalent to the squares described upon the sides which contain the right angle . Let ABC be a right angled trian- gle having the right angle BAC ; the square described upon the ...
... described upon the side sub- tending the right angle , is equivalent to the squares described upon the sides which contain the right angle . Let ABC be a right angled trian- gle having the right angle BAC ; the square described upon the ...
Página 31
... described upon one of the sides of a triangle , be equivalent to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle . If the square described upon BC , one of the sides of the ...
... described upon one of the sides of a triangle , be equivalent to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle . If the square described upon BC , one of the sides of the ...
Página 32
... described upon the given straight line AB . PROP . II . PROB . From a given point to draw a straight line equal to a given straight line . Let A be the given point , and BC the gi- ven straight line ; it is required to draw , from the ...
... described upon the given straight line AB . PROP . II . PROB . From a given point to draw a straight line equal to a given straight line . Let A be the given point , and BC the gi- ven straight line ; it is required to draw , from the ...
Página 37
... described from A as a centre , with a radius equal to AB , the other given side , would cut BC on opposite sides of C ' ; so that only B A one obtuse angled triangle could be formed ; that is , the triangle BC'A will be the triangle ...
... described from A as a centre , with a radius equal to AB , the other given side , would cut BC on opposite sides of C ' ; so that only B A one obtuse angled triangle could be formed ; that is , the triangle BC'A will be the triangle ...
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Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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...
Página 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.
Página 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...
Página 134 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.