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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... Scholium , to each proposition . Several Theorems , Lemmas , Corollaries , and Scholiums , are interspersed throughout the whole work , not contained in any previous edition . A few useful Problems , especially in Surveying , are also ...
... Scholium , to each proposition . Several Theorems , Lemmas , Corollaries , and Scholiums , are interspersed throughout the whole work , not contained in any previous edition . A few useful Problems , especially in Surveying , are also ...
Seite 2
... Scholium is a remark or observation made on some foregoing propo- sition or premises . 13. An Hypothesis is a supposition assumed to be true , in order to argue from , or to found upon it the reasoning and demonstration of some pro ...
... Scholium is a remark or observation made on some foregoing propo- sition or premises . 13. An Hypothesis is a supposition assumed to be true , in order to argue from , or to found upon it the reasoning and demonstration of some pro ...
Seite 10
... SCHOLIUM . C D B The equality of the triangles ADC , BDC , proves also that AD is equal to BD , and the angle ADC equal to the angle BDC ; hence , these two are right angles : hence , the line bisecting the vertical angle of an ...
... SCHOLIUM . C D B The equality of the triangles ADC , BDC , proves also that AD is equal to BD , and the angle ADC equal to the angle BDC ; hence , these two are right angles : hence , the line bisecting the vertical angle of an ...
Seite 16
... SCHOLIUM . This may be demonstrated without producing any of the sides : thus , the line BC , for example , is the shortest distance from B to C ; therefore BC is less than BA + AC , or BA + AC > BC . PROP . XIV . THEOR . If from the ...
... SCHOLIUM . This may be demonstrated without producing any of the sides : thus , the line BC , for example , is the shortest distance from B to C ; therefore BC is less than BA + AC , or BA + AC > BC . PROP . XIV . THEOR . If from the ...
Seite 21
... SCHOLIUM . The angles just spoken of , when compared with each other , assume dif- ferent names . BGH , GHD , we have already named interior angles on the same side ; AGH , GHC , have the same name ; AGH , GHD , are called alternate ...
... SCHOLIUM . The angles just spoken of , when compared with each other , assume dif- ferent names . BGH , GHD , we have already named interior angles on the same side ; AGH , GHC , have the same name ; AGH , GHD , are called alternate ...
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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.