## 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 ii

For , what has methanic Trades to do with Latin ? any more than a

Porter or Carman with Logic ; it may indeed complete him a Pedant or Coxcomb ,

but can never be of real use in his Profession ; even suppose he had made a ...

For , what has methanic Trades to do with Latin ? any more than a

**common**Porter or Carman with Logic ; it may indeed complete him a Pedant or Coxcomb ,

but can never be of real use in his Profession ; even suppose he had made a ...

Page 309

But , the Angle EAH is

Parallelograms are equal 15. 1 . wherefore , EFH – BCD . Also , the Angle AEF =

ABC , and AHF = ADC . - 4.1 . therefore AEFH is similar to the whole Par . ABCD -

Def.i .

But , the Angle EAH is

**common**to both ; and , the opposite Angles ofParallelograms are equal 15. 1 . wherefore , EFH – BCD . Also , the Angle AEF =

ABC , and AHF = ADC . - 4.1 . therefore AEFH is similar to the whole Par . ABCD -

Def.i .

Page 363

Let AGHD and FHIL be R G Parallelopipeds ; whose Bafes , ABCD and I KLM ,

are equal , and in the same Plane ; and the Top , EFGH ,

have no other Plane

Let AGHD and FHIL be R G Parallelopipeds ; whose Bafes , ABCD and I KLM ,

are equal , and in the same Plane ; and the Top , EFGH ,

**common**to both ; buthave no other Plane

**common**. I say , that the Parallelopiped AGHD , is equal to ... Page 364

When the Parallelopipeds have no Face

Parallelopipeds AOMD YK and EMKG , be between the same parallel Planes ,

ARH and NQI ; consequently , they have equal AlR titude ; and , let the Base ,

ABCD ...

When the Parallelopipeds have no Face

**common**, nor similar Figures . Let theParallelopipeds AOMD YK and EMKG , be between the same parallel Planes ,

ARH and NQI ; consequently , they have equal AlR titude ; and , let the Base ,

ABCD ...

Page 383

and anAngleAEB , equal DBE , ( each

CEB , or EBF ; being contained by the Diagonal of a Square , ( CE ) and the

Hypothenuse ( BE ) of a right angled Triangle , under the Side and Diagonal , BC

, and ...

and anAngleAEB , equal DBE , ( each

**common**to two Pyramids ) each equalCEB , or EBF ; being contained by the Diagonal of a Square , ( CE ) and the

Hypothenuse ( BE ) of a right angled Triangle , under the Side and Diagonal , BC

, and ...

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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.