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 σελίδες |
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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 ...
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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 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 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...
Σελίδα 68 - THE angles in the same segment of a circle are equal to one another...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 75 - If a straight line touch a circle, and from the point of contact a...
Σελίδα 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...
Σελίδα 134 - EQUIANGULAR parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Σελίδα 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.