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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Σελίδα 8
... straight line . " " COR . Hence two straight lines cannot inclose a space . Neither can two " straight lines have a common segment ; that is , they cannot coincide " in part , without coinciding altogether . " 4. A superficies is that ...
... straight line . " " COR . Hence two straight lines cannot inclose a space . Neither can two " straight lines have a common segment ; that is , they cannot coincide " in part , without coinciding altogether . " 4. A superficies is that ...
Σελίδα 9
... straight line standing on another straight line makes the adjacent angles equal to one another , each of the angles is called a right angle ; and the straight line which stands on the other , is called a perpendicu- lar to it . 8. An ...
... straight line standing on another straight line makes the adjacent angles equal to one another , each of the angles is called a right angle ; and the straight line which stands on the other , is called a perpendicu- lar to it . 8. An ...
Σελίδα 11
... straight lines are such as are in the same plane , and which being produced ever so far both ways , do not meet . POSTULATES . - 1. LET it be granted that a straight line ... straight line may be produced to any length in a straight line . 3 ...
... straight lines are such as are in the same plane , and which being produced ever so far both ways , do not meet . POSTULATES . - 1. LET it be granted that a straight line ... straight line may be produced to any length in a straight line . 3 ...
Σελίδα 12
... straight line . Let AB be the given straight line ; it is required to describe an equi- lateral triangle upon it . • From the centre A , at the dis- tance AB , describe ( 3. Postulate ) the circle BCD , and from the cen- tre B , at the ...
... straight line . Let AB be the given straight line ; it is required to describe an equi- lateral triangle upon it . • From the centre A , at the dis- tance AB , describe ( 3. Postulate ) the circle BCD , and from the cen- tre B , at the ...
Σελίδα 13
... straight line AL is equal to BC . Wherefore , from the given point A , a straight line AL has been drawn equal to the given straight line BC . PROP . III . PROB .. From the greater of two given straight lines to cut off a part equal to ...
... straight line AL is equal to BC . Wherefore , from the given point A , a straight line AL has been drawn equal to the given straight line BC . PROP . III . PROB .. From the greater of two given straight lines to cut off a part equal to ...
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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 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
Δημοφιλή αποσπάσματα
Σελίδα 41 - 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 70 - 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 45 - Again, because the angle at B is half a right angle, and FDB a right angle, for it is equal...
Σελίδα 91 - 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...
Σελίδα 273 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Σελίδα 25 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Σελίδα 130 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Σελίδα 61 - THE diameter is the greatest straight line in a circle; and, of all others, that which is nearer to the centre is always greater than one more remote ; and the greater is nearer to the centre than the less.* Let ABCD be a circle, of which...