A Royal Road to Geometry: Or, an Easy and Familiar Introduction to the Mathematics. ... By Thomas Malton. ... |
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Page 334
I. A SOLID is a Body , having length , breadth , and thickness ; and is bounded by
Planes , or curved Surfaces , or both . As X. X A -B Def . II . A Plane ( or Right Line
) is parallel to another Plane , which , being produced infinitely , would never ...
I. A SOLID is a Body , having length , breadth , and thickness ; and is bounded by
Planes , or curved Surfaces , or both . As X. X A -B Def . II . A Plane ( or Right Line
) is parallel to another Plane , which , being produced infinitely , would never ...
Page 335
V. If a Plane ( or Right Line ) be neither parallel nor perpendicular to another
Plane , it is faid to incline to the other Plane . The inclination of one Plane to the
other is the acute Angle ABC , made by the Section of another Plane , DEC ;
cuting ...
V. If a Plane ( or Right Line ) be neither parallel nor perpendicular to another
Plane , it is faid to incline to the other Plane . The inclination of one Plane to the
other is the acute Angle ABC , made by the Section of another Plane , DEC ;
cuting ...
Page 337
Every part of a Right Line is in the same Plane . i . e . One part of a Right Line
cannot be in any Plane , and another part of the Line out of that Plane . B For , if it
was poflible , a Right Line does not a agree with a Plane in every Point ;
agreeable ...
Every part of a Right Line is in the same Plane . i . e . One part of a Right Line
cannot be in any Plane , and another part of the Line out of that Plane . B For , if it
was poflible , a Right Line does not a agree with a Plane in every Point ;
agreeable ...
Page 345
From any given Point , * to draw a Right Line perpendicular to a Plane , in which
that point is not fituated . Let A be the given Point , and BEC a Plane . In the Plane
BEC , draw , at pleasure , the Right Line BC , and , from A , B draw the Right ...
From any given Point , * to draw a Right Line perpendicular to a Plane , in which
that point is not fituated . Let A be the given Point , and BEC a Plane . In the Plane
BEC , draw , at pleasure , the Right Line BC , and , from A , B draw the Right ...
Page 350
I say , the Planes , CAD and EAF , are perpendicular to ÇEDF . Dem . Now ,
because A B is perpendicular to the Plane CEF ( by Hypotbesis ) it does not
incline to it on any Side - Def.3 . But , the Line AB is in the Plane CAD ; and it is
also in the ...
I say , the Planes , CAD and EAF , are perpendicular to ÇEDF . Dem . Now ,
because A B is perpendicular to the Plane CEF ( by Hypotbesis ) it does not
incline to it on any Side - Def.3 . But , the Line AB is in the Plane CAD ; and it is
also in the ...
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A Royal Road to Geometry: Or, an Easy and Familiar Introduction to the ... Thomas Malton No preview available - 2016 |
Common terms and phrases
ABCD added alſo Altitudes analogous Area Baſe becauſe biſected Book called Center Chord Circle Circumference common Cone conf conſequently Conſtruction contained cuting Cylinder Demonſtration deſcribe Diagonal Diameter difference divided draw drawn equal Euclid evident extreme fame Feet Figure firſt formed four fourth given given Line greater half Hence Inches inſcribed join laſt leſs manner mean meaſure multiplied muſt oppoſite parallel Parallelogram Parallelopiped Pentagon perpendicular Plane Point Poligon Priſm Prob PROBLEM produced Proportion Propoſition proved Pyramid Quantities Radius Ratio Rect Rectangle reſpectively Right Angles Right Line ſame ſame Ratio ſay ſeeing Segment Sides ſimilar Solid ſome Sphere Square ſuch Surface taken Terms THEOREM third thoſe touch Triangle uſe wherefore whole whoſe
Popular passages
Page 124 - When you have proved that the three angles of every triangle are equal to two right angles...
Page 221 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 285 - EG, let fall from a point in the circumference upon the diameter, is a mean proportional between the two segments of the diameter DS, EF (p.
Page 284 - IN a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another.
Page 186 - From this it is manifest, that if one angle of a triangle be equal to the other two, it is a right angle, because the angle adjacent to it is equal to the same two; and when the adjacent angles are equal, they are right angles.
Page 248 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D; and read, A is to B as C to D.
Page 161 - In any triangle, if a line be drawn from the vertex at right angles to the base; the difference of the squares of the sides is equal to the difference of the squares of the segments of the base.
Page 160 - In any isosceles triangle, the square of one of the equal sides is equal to the square of any straight line drawn from the vertex to the base plus the product of the segments of the base.
Page 250 - Ratios that are the same to the same ratio, are the same to one another. Let A be to B as C is to D ; and as C to D, so let E be to F.
Page 124 - Angles, taken together, is equal to Twice as many Right Angles, wanting four, as the Figure has Sides.
Bibliographic information
| Title | A Royal Road to Geometry: Or, an Easy and Familiar Introduction to the Mathematics. ... By Thomas Malton. ... |
| Author | Thomas Malton |
| Publisher | author, and sold, 1774 |
| Original from | Oxford University |
| Digitized | 19 Apr 2006 |
| Length | 440 pages |
| Export Citation | BiBTeX EndNote RefMan |