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 Sperical TrigonometryW.E. Dean, 1844 - 317 sider |
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Resultat 1-5 av 53
Side 4
... taken in their utmost generality , and when no assistance can be received from diagrams . As it is plain that the concise language of Algebra is directly calculated to remedy this in- convenience , I have endeavoured to introduce it ...
... taken in their utmost generality , and when no assistance can be received from diagrams . As it is plain that the concise language of Algebra is directly calculated to remedy this in- convenience , I have endeavoured to introduce it ...
Side 5
... 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 proposition ; in which some property is asserted , and the truth of it required to be ...
... 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 proposition ; in which some property is asserted , and the truth of it required to be ...
Side 7
... taken away from it . In like manner , A - B + C , or A + C - B , signifies that A and C are to be added together , and that B is to be subtracted from their sum . 22. Multiplication is expressed by an oblique cross , by a point , or by ...
... taken away from it . In like manner , A - B + C , or A + C - B , signifies that A and C are to be added together , and that B is to be subtracted from their sum . 22. Multiplication is expressed by an oblique cross , by a point , or by ...
Side 8
... taken , the straight line between them lies wholly in that superficies . 6. A plane rectilineal angle is the inclination of two straight lines to one another , which meet together , but are not in the same straight line . D B E N. B. ...
... taken , the straight line between them lies wholly in that superficies . 6. A plane rectilineal angle is the inclination of two straight lines to one another , which meet together , but are not in the same straight line . D B E N. B. ...
Side 11
... taken from equals , the remainders are equal . 4. If equals be added to unequals , the wholes are unequal . 5. If equals be taken from unequals , the remainders are unequal . 6. Things which are doubles of the same thing , are equal to ...
... taken from equals , the remainders are equal . 4. If equals be added to unequals , the wholes are unequal . 5. If equals be taken from unequals , the remainders are unequal . 6. Things which are doubles of the same thing , are equal to ...
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Vanlige uttrykk og setninger
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 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 touches the circle triangle ABC triangle DEF wherefore
Populære avsnitt
Side 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...
Side 68 - THE angles in the same segment of a circle are equal to one another...
Side 23 - Straight lines which are parallel to the same straight line are parallel to one another. Triangles and Rectilinear Figures. The sum of the angles of a triangle is equal to two right angles.
Side 74 - 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.
Side 78 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Side 9 - UPON the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.
Side 75 - If a straight line touch a circle, and from the point of contact a...
Side 18 - AT a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle. Let AB be the given straight line, and A...
Side 134 - EQUIANGULAR parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Side 136 - AB is (7. 5.) to AD, as AE to AG ; and DC to CB, as GF to FE; and also CD to DA, as FG to GA ; therefore the sides of the parallelograms ABCD, AEFG about the equal angles are proportionals; and they are therefore similar to one another (1.