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 σελίδες |
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Αποτελέσματα 1 - 5 από τα 79.
Σελίδα 8
... meet together , but are not in the same straight line . Α D E B C N. B. ' When several angles are at one point B , any one of them is ex- pressed by three letters , of which the letter that is at the vertex of the an- gle , that is , at ...
... meet together , but are not in the same straight line . Α D E B C N. B. ' When several angles are at one point B , any one of them is ex- pressed by three letters , of which the letter that is at the vertex of the an- gle , that is , at ...
Σελίδα 11
... meet . POSTULATES . 1. 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 ...
... meet . POSTULATES . 1. 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 ...
Σελίδα 27
... meet to- wards B , D. In like manner it may be demonstrated that they do not meet towards A , C ; but those straight lines which meet neither way , though produced ever so far , are parallel ( 30. Def . ) E B G C F D to one another . AB ...
... meet to- wards B , D. In like manner it may be demonstrated that they do not meet towards A , C ; but those straight lines which meet neither way , though produced ever so far , are parallel ( 30. Def . ) E B G C F D to one another . AB ...
Σελίδα 28
... meet on the side of EF on which the two angles are that are less than two right angles . For , if not , KL and CD are either parallel , or they meet on the other side of EF ; but they are not parallel ; for the angles KGH , GHC would ...
... meet on the side of EF on which the two angles are that are less than two right angles . For , if not , KL and CD are either parallel , or they meet on the other side of EF ; but they are not parallel ; for the angles KGH , GHC would ...
Σελίδα 29
... meet towards L and D , they must meet if produced towards K and C. COR . 2. If BGH is a right angle , GHD will be a right angle also ; therefore every line perpendicular to one of two parallels , is perpendicular to the other . COR . 3 ...
... meet towards L and D , they must meet if produced towards K and C. COR . 2. If BGH is a right angle , GHD will be a right angle also ; therefore every line perpendicular to one of two parallels , is perpendicular to the other . COR . 3 ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 22 - Any two sides of a triangle are together greater than the third side.
Σελίδα 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.
Σελίδα 35 - Parallelograms upon the same base and between the same parallels, are equal to one another.