## A Royal Road to Geometry: Or, an Easy and Familiar Introduction to the Mathematics. ... By Thomas Malton. ... |

### From inside the book

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Page 77

24. and 25. reduced the given Figure's to Squares ; i . e . having found the side of

a Square , equal to each Figure ,

equal io them , and forming a Right Angle , ABE . Produce AB or EB , indefinite ...

24. and 25. reduced the given Figure's to Squares ; i . e . having found the side of

a Square , equal to each Figure ,

**respectively**, make A B and BE**respectively**equal io them , and forming a Right Angle , ABE . Produce AB or EB , indefinite ...

Page 137

and DG = AC , by Suppofition ; the Sides , AB , AC , are

DG ; and the Angle BAC = EDG . - • Hyp . Wh . EG BC and the Triangle DEG =

ABC . - -8 . consequently , the remaining Angles , of the one , are equal to the ...

and DG = AC , by Suppofition ; the Sides , AB , AC , are

**respectively**equal to DE ,DG ; and the Angle BAC = EDG . - • Hyp . Wh . EG BC and the Triangle DEG =

ABC . - -8 . consequently , the remaining Angles , of the one , are equal to the ...

Page 344

If two Right Lines , cuting or meeting each other , be

other Right Lines , also meeting or cuting one another , though not in the same

Plane with the first , they shall contain equal Angles . Let the two Right Lines , AB

...

If two Right Lines , cuting or meeting each other , be

**respectively**parallel to twoother Right Lines , also meeting or cuting one another , though not in the same

Plane with the first , they shall contain equal Angles . Let the two Right Lines , AB

...

Page 348

If two Right Lines , cuting or meeting each other , be parallel to two other Right

Lines , also meeting each other , not in the same Plane with the first two ; Planes

passing through each two Lines ,

Lines ...

If two Right Lines , cuting or meeting each other , be parallel to two other Right

Lines , also meeting each other , not in the same Plane with the first two ; Planes

passing through each two Lines ,

**respectively**, are parallel . H Let , the RightLines ...

Page 370

Solid Angles , contained by three Plane Angles , each , of which , two and two (

one in each ) are equal ,

Planes have equal Inclination to each other ,

Solid Angles , contained by three Plane Angles , each , of which , two and two (

one in each ) are equal ,

**respectively**, are equal to one another . Because thePlanes have equal Inclination to each other ,

**respectively**( by the Theorem ) ...### What people are saying - Write a review

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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.