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

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Page 18

I also particularly advise him , when he meets with any

he has not a clear Idea , to turn immediately back to the Definition of it ; he may

depend on it , that the time will not be entirely loft . Several of the

I also particularly advise him , when he meets with any

**Term**hereafter , of whichhe has not a clear Idea , to turn immediately back to the Definition of it ; he may

depend on it , that the time will not be entirely loft . Several of the

**Terms**which I ... Page 67

Now , in both these Cases , the two extreme

. 4 and 15 , and the two middle

middle

the ...

Now , in both these Cases , the two extreme

**Terms**, i . e . the first and the last , viz. 4 and 15 , and the two middle

**Terms**, 6 and 10 , remain the same ; only , themiddle

**Terms**have changed places ; but , the second multiplied by the third crthe ...

Page 242

It was not the Design , of those Geometers who made use of this

Analogy , in abstract , but only , to ... which is only another

Ratio for Proportion ; which ,

It was not the Design , of those Geometers who made use of this

**Term**, to defineAnalogy , in abstract , but only , to ... which is only another

**Term**for Ratio , orRatio for Proportion ; which ,

**Terms**, are fynonimous , and equally expressive . Page 244

fequent ; Def , V. ) But , fince the Consequent of the first Ratia inay , also , be the

Antecedent of the second ( as A : B :: B : C ) three

Analogy ; in which cafe , it is neceflary that they are all of the fame species or ...

fequent ; Def , V. ) But , fince the Consequent of the first Ratia inay , also , be the

Antecedent of the second ( as A : B :: B : C ) three

**Terms**are fuificient to constituteAnalogy ; in which cafe , it is neceflary that they are all of the fame species or ...

Page 245

PROPORTIONALS are such Quantities as are in the fame Ratio ; discretely or

continual . Proportionals confift , at least , of three

are usually symbolized by Right Lines ; or by Characters , as A : B :: C : D , the

Ratio ...

PROPORTIONALS are such Quantities as are in the fame Ratio ; discretely or

continual . Proportionals confift , at least , of three

**Terms**, or Quantities ; whichare usually symbolized by Right Lines ; or by Characters , as A : B :: C : D , the

Ratio ...

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### 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.