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 TrigonometryJ.P. Lippincott & Company, 1855 - 318 sider |
Inni boken
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 . E. 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 . E. 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 . Α D E B C ...
... 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 . Α D E B C ...
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 definition 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 Let the straight magnitudes meet 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 51 - 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 of the line between the points of section, is equal to the square of half the line.
Side 29 - 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 12 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line.
Side 11 - Let it be granted that a straight line may be drawn from any one point to any other point. 2. That a terminated straight 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.
Side 72 - To draw a straight line from a given point, either without or in the circumference, which shall touch a given circle. First, let A be a given point without the given circle BCD : it is required to draw a straight line from A which shall touch the circle.
Side 84 - 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 80 - 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 22 - Any two sides of a triangle are together greater than the third side.
Side 53 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Side 35 - Parallelograms upon the same base and between the same parallels, are equal to one another.