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 |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 52.
Σελίδα 7
... remaining , when a part equal to B has been 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 ...
... remaining , when a part equal to B has been 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 ...
Σελίδα 14
... remaining angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the angle ABC to the angle DEF , and the angle ACB to the angle DFE . Therefore , if two triangles have two sides of the ...
... remaining angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the angle ABC to the angle DEF , and the angle ACB to the angle DFE . Therefore , if two triangles have two sides of the ...
Σελίδα 20
... remaining angle ABE is equal ( 3. Ax . ) to the remaining angle ABD , the less to the greater , which is im- possible ; therefore BE is not in the same straight line with BC . And in like manner , it may be demonstrated , that no other ...
... remaining angle ABE is equal ( 3. Ax . ) to the remaining angle ABD , the less to the greater , which is im- possible ; therefore BE is not in the same straight line with BC . And in like manner , it may be demonstrated , that no other ...
Σελίδα 21
... remaining angles to the remaining angles each to each , to which the equal sides are oppo- site ; wherefore the angle BAE is equal to the angle ECF ; but the angle ECD is greater than the an- gle ECF ; therefore the angle ECD , that is ...
... remaining angles to the remaining angles each to each , to which the equal sides are oppo- site ; wherefore the angle BAE is equal to the angle ECF ; but the angle ECD is greater than the an- gle ECF ; therefore the angle ECD , that is ...
Σελίδα 28
... remaining angle AGH is equal to the remaining angle GHD ; and they are alternate angles ; therefore AB is parallel to CD . COR . Hence , when two straight lines are perpendicular to a third line , they will be parallel to each other ...
... remaining angle AGH is equal to the remaining angle GHD ; and they are alternate angles ; therefore AB is parallel to CD . COR . Hence , when two straight lines are perpendicular to a third line , they will be parallel to each other ...
Άλλες εκδόσεις - Προβολή όλων
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 line BC magnitudes meet opposite angle parallel parallelogram parallelopiped perpendicular plane 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 spherical angle spherical triangle square straight line AC THEOR third 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...