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be thus conceived : and A be Similar to B; all Things in A will be the fame with thole in B.
Since a Quantity cannot be underftood, otherwife, than by affuming feme other Quantity to refer it to- Simi- lar Things, notwithstanding their Similitude, may differ in Quantity : And fince, in Similar Things, there is nothing wherein they differ, befide the Quantity 5 Quantity ftfelf is the Internal Difference o£ Similar Things. See Similitude. Similar Warts, as A a, have the fame Ratio to their Wholes B b ; and if the Wholes have the fame Ratio to the Parts, the Parts are Similar. Similar 'Parts A a, are to each other as their Wholes B b. See Part.
Similar Retlangles^ are thofe which have their Sides about the equal Angles, proportional. See Rectangle.
Hence i°. All Squares muft be Similar ReBangles. See Square. — 2°. All Similar ReBangles are, to each other, as the Square of their homologous Sides.
Similar Triangles,- are iiich as have all their three An- gles reflectively equal to each other. See Triangle.
Hence i°. All Similar Triangles have their Sides about the equal Angles, proportional. — 2 Q . All Similar "tri- angles are, to each other, as the Squares of their homolo- gous Sides.
Similar Polygons are thofe, whofe Angles are equal, and their Sides proportional.
And the like of other funilar rectilinear Figures. See Polygon, and Rectilineal Figure.
Hence, all Similar 'Polygons are, to each other, as the Squares of the homologous Sides.
Similar Arches, are fuch as arc Similar, or equal Parts of their refpective Circumferences.
Similar Segments of Circles, are fuch as contain equal Angles. See Segment.
Similar Conic-Seclians, are thofe whofeDiameters make Angles equal to thofe of their Ordinates 5 i. e. thofe which are equilateral and equiangular.
Similar Plain Numbers, are thofe which may he ranged into Similar Reel-angles 5 i. e. into Rectangles, whofe Sides are proportional .- As 6 multiplied by 2, and 12 by 4; the Product of one whereof is 12, and the other 48, arc Similar Numbers.
Similar Solid Numbers, are thofe whofe little Cubes may be fo ranged as to make Similar and Rectangular Parallelipipeds.
In all Similar Figures, the homologous Angles are equal 5 and the homologous Sides proportional. All regu- lar Figures, and Similar irregular ones, are in a duplicate Ratio of their homologous Sides. Circles, and Similar Fi- gures, inscribed in them, are, to each other, as the Squares of the Diameter. See Figure.
Similar Angles, are alfo equal Angles. In folid Angles, when the Planes, under which they are contained, are equal both in Number and Magnitude, and are dif- poled m the fame Order 5 they are Similar-, and confe- quently equal. See Angle.
In Similar Triangles, and Parallelograms, the Alti- tudes are proportional to the homologous Sides ; and the Bales are cut proportionably by thole Sides. See Triangle, l$c.
Similar. T)ifeafe, a Difeafe of fome fimple, folid Part of the Body ; as of a Fibre, with regard to its Ten- fion or Flaccidity; of a Membrane ; a nervous Canal, ££?c See Disease.
Similar Warts, in Anatomy, thofe Parts of the Body which, at firft Sight, appear to confift of like Parts, or Parts of the lame Nature : Of thele we ufually reckon Ten, viz. The Bones, Cartilages, Ligaments, Membranes, Fibres, Nerves, Arteries, Veins, Flelh, and Skin : Each of which lee under its proper Article. Dr. Grew, in his Anatomy of Plants, obferves, that thele have, likewiie, their Similar, and Organical Parts. See Parts.
SIMILE, or SIMILITUDE, in Rhetoric,^, a Com- panion of two Things, which, though different in other Relpects, yet agree in lome one : As, He fhall be like a Tree planted by the Water-fide, &c. The Difference be- tween a Simile, and a Companfon, confifts in this ; That the Simile properly belongs to what we call the Quality of the Thing, and the Comparifcu to the Quantity. See' Com- parison.
SIMILITUDE, in Arithmetic, Geometry, &c. the Rela- tion of two Things fvmilar to each other ; or which are only . diflinguillrablebyCom-prefence. SeeSiMiLE. The Notion of Similitude, which now makes fome Figure in Geometry, &G. is owing to M. Leibnitz : 'Twill be rendered eafy by the following Inftance. Suppofe two Watches perfectly alike ; the one belonging to Caius, the other to Gracchus. If, now, Cains pull out his Watch in Prefence of Gracchus ; the latter wiil be furprized, and fancy it his own ; but he will perceive it different from hts own, upon pulling out his own: that is, Gracchus di&ingmihcs Cairn's Watch from his own, by their Com-prefence ; or, by applying the one im- mediately to the ether.
Euclid, and after him mofl other Authors, demon Arated all Ihings from the fole Principle of Congruity : j^A, in lieu hereof, fubftitutes that of Similitude ; which, he tells us, was communicated to him by M. Leibnitz, and which he finds of very notable Ule in Geometry, as ferving to demonftrate many Things directly, which are only de- monftrable from the Principle of Congruity by an Am- bages.
SIMONIACAL is applied to a Perfon guilty of Simonv; or of purchafing a Benefice, or other (acred Matter, with Money. See Simony. A Simoniacal Perfon convict, is 1 infamous, and incapable of holding any Benefice.
SIMONIANS, a Sect of ancient Hereticks, the firft that ever difturb'd Chriflianity ; if they might be laid to do lo, who were little more than mere Phiiofbphers, and made Profeflion of Magic. Simon Magus, f often menti- oned in the Alls, was their Leader, and died under the Emperor Nero; St. Peter ftill furviving : So that Clemens Alexandrimts is miftaken, when he makes Simon oofterior to Marcion. St. Epiphanius fays exprefly, That 'the firft Hereiy was let on foot by Simon the Magician, born in a little City of Samaria, who pretended to be the great Virtue and Power of God, fent from Heaven to Earth. Among the Samaritans he made bimlelf pals fur God the Father, and among the Jews, for the Son. He patch'd up a Kind of medly Syftem, out of the Philofophy of Plate-, the religious Fables of the Heathens, and Cfiriftianity -. Particularly, from the Platonip he borrow'd abundance of Things relating to the Wurfhip of Angels, which he perverted to Ufes of Magic ; pretending, there was no Salvation, but by the Invocation of Angels, who were, as it were, the Mediators between God and Man: To which iiiperftitious Worfhip of Angels it is that St. Paul fecms to refer in his Epillle to the Colojjiam. The Gnoftcks, where- of the fame Simon was the "Father, adopted the fame Practice ot worfhipping Angels, and even improved on it. See Gnosticks.
SIMONY, the Crime of trading with facred Things, particularly of purchafing a Benefice with Money. By' the Bnglifh Canons, Anno 1219, Simony is not only com- mitted by an Agreement for Money in Hand, or to be paid yearly; but for any other Profit or Emolument; any Re- ward, Gift, or Benefit, directly or indirectly ; or by Rea- ibn of any Promife, Grant, Bond, &c. and this, either in Acceptance of a Living, or in an Exchange or Refignation. The Penalty, by our Laws, is, That the corrupt Patron fhall forfeit the next Prelentation to the King, and twd Years Value of the Living; and the corrupt Incumbent, be for ever difabled to hold the Living.
Simony is committed by the Buying or Selling the Sa- crament, Baptijm, Ordination, Ablbluuon, as well as of the Nomination and Collation to Benefices, a Place in a Mo- nastery, or the like. Some have pretended it to be fufrkient, that the Ordination were gratuitous; and that for the reft, the Revenues might be bought and fold as a Temporal Thing: But the Cununs of leveral Councils have con- demned this fubtle Diftinction ; fince the Revenues are at- tach'd to an Ecclefiaftical Office purely Spiritual. The Cafuiits diftinguifh three Kinds of Simony. Mental Si- mony, is that which flicks in the mere Will, and Inclina- tion, without ever breaking forth into Act : As when a Pre- fent is made to a Collator, without taking any Notice that we expect a Benefice from him. This Kind of Simony is only punifhable in foro Confcienti^e, Conventional Simony is where there is an exprels Act, and a formal Bargain^ though it never come to an Execution. Real Simony, is where the Convention is executed on both Sides, which lalt is the moft criminal of them ail. The Penalty of Simony is Depofition in a Clerk, and Excommunication in a Lay- man. 'Tis a Maxim among the Romifh Canoniits, That there is no Simony in the Courr of Rome ; in Regard, tho Pope acts there as an abfolute Sovereign. They alio lay, That Resignations, in favorem, are not to be admitted but by the Pope, as favouring a little of Simony. On thefe Occa- fiorts, however, they fwear, That there has been no Deceit, Collufion, or Simony, or other- illegal Covenant. Peter Da- »^2?«diftinguiihes three Kinds of Simony ; that of Mo- ney, that of the Tongue, and that o* Services. Simony of Money, or per mumis 4 manli, is where Money is really paid down for a Benefice : He adds, That 'tis likewiie committed, by expending Money to live at Court to obtain a Benefice. Simony of the Tongue, or per muniis a lingua* confifts in flattering the Collator, or making one's felf agreeable by Complaifance and Commendation. Simony of Services, or per mumis ah obfequio. confifts in the doing them good Offices to obtain a Benefice. The Word is bor- row'd from Simon Magus, who is mention'd in the Acts of the Apoftles, as offering to buy the Power of working Mi- racles with Money.
It was agreed, by all thejuftices, T'rin.Ocl. Jac.Primi, That if the Patron prcfentcd any Perfon to a Benefice with
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